Edit Profile (opens in new tab) Borgs, Christian Co-Author Distance Author ID: borgs.christian Published as: Borgs, Christian; Borgs, C. Homepage: https://www.microsoft.com/en-us/research/people/borgs/?from=http%3A%2F%2Fresearc... External Links: MGP · Wikidata · Google Scholar · dblp Documents Indexed: 93 Publications since 1986, including 8 Additional arXiv Preprints 1 Contribution as Editor Co-Authors: 89 Co-Authors with 91 Joint Publications 2,953 Co-Co-Authors all top 5 Co-Authors 3 single-authored 76 Chayes, Jennifer Tour 10 Kotecký, Roman 7 Lovász, László 7 Teng, Shang-Hua 6 Berger, Noam 6 Cohn, Henry Lee 5 Bollobás, Béla 5 Mirrokni, Vahab S. 5 Saberi, Amin 5 Sós, Vera Turán 5 Spencer, Joel H. 5 Vesztergombi, Katalin 4 Biskup, Marek 4 Mertens, Stephan 4 Pittel, Boris G. 4 Riordan, Oliver Maxim 4 Slade, Gordon 4 Tetali, Prasad 4 van der Hofstad, Remco W. 3 Andersen, Reid 3 Bayati, Mohsen Fathollah 3 Brautbar, Michael 3 Imbrie, John Z. 3 King, Christopher Kevin 3 Sen, Subhabrata 2 Alimohammadi, Yeganeh 2 Dhara, Souvik 2 Fröhlich, Jürg Martin 2 Helmuth, Tyler 2 Hopcroft, John Edward H. 2 Immorlica, Nicole 2 Kalai, Adam Tauman 2 Kesten, Harry 2 Kleinberg, Robert D. 2 Kleinwaks, Logan J. 2 Madras, Neal 2 Montanari, Andrea 2 Nair, Chandra 2 Papadimitriou, Christos Harilaos 2 Perkins, Will 2 Roch, Sébastien 2 Waxler, Roger 2 Zecchina, Riccardo 2 Zhao, Yufei 1 Balcan, Maria-Florina 1 Baldassi, Carlo 1 Braverman, Mark 1 Chaudhari, Pratik 1 Choromanska, Anna 1 Daskalakis, Constantinos 1 Doroudi, Sherwin 1 Dyer, Martin E. 1 Gamarnik, David 1 Ganesh, Ayalvadi J. 1 Ganguly, Shirshendu 1 Gaudio, Julia 1 Harchol-Balter, Mor 1 Holden, Nina 1 Hopcraft, John 1 Jȩdrzejewski, Janusz 1 Kahn, Jeff D. 1 Kanoria, Yash 1 Kanoria, Yashodhan 1 Karrer, Brian 1 Kim, Jeong Han 1 LeCun, Yann 1 Lovász, László Miklós 1 Lucier, Brendan 1 Marple, Adrian 1 Medved’, Igor 1 Meeder, Brendan 1 Mossel, Elchanan 1 Nill, Florian 1 Petti, Samantha 1 Randall, Dana J. 1 Ravi, Ramamoorthi 1 Reagans, Ray 1 Sagun, Levent 1 Sayedi, Amin 1 Shah, Devavrat 1 Soatto, Stefano 1 Szegedy, Balázs 1 Ueltschi, Daniel 1 Veitch, Victor 1 Wilson, David Bruce 1 Xu, Kuang 1 Yu, Christina Lee 1 Zadik, Ilias 1 Zhao, Geng all top 5 Serials 11 Communications in Mathematical Physics 11 Random Structures & Algorithms 8 Journal of Statistical Physics 7 The Annals of Probability 3 Journal of Mathematical Physics 2 Journal of Physics A: Mathematical and General 2 Combinatorics, Probability and Computing 2 Internet Mathematics 1 Advances in Mathematics 1 The Annals of Statistics 1 Journal of Economic Theory 1 Operations Research 1 Theoretical Computer Science 1 Transactions of the American Mathematical Society 1 European Journal of Combinatorics 1 Combinatorica 1 Probability Theory and Related Fields 1 SIAM Journal on Discrete Mathematics 1 Geometric and Functional Analysis. GAFA 1 Games and Economic Behavior 1 Nuclear Physics. B. Proceedings Supplements 1 Annals of Combinatorics 1 Annals of Mathematics. Second Series 1 Probability in the Engineering and Informational Sciences 1 Journal of Machine Learning Research (JMLR) 1 Journal of Statistical Mechanics: Theory and Experiment all top 5 Fields 37 Probability theory and stochastic processes (60-XX) 36 Combinatorics (05-XX) 36 Statistical mechanics, structure of matter (82-XX) 25 Computer science (68-XX) 11 Operations research, mathematical programming (90-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Statistics (62-XX) 5 Quantum theory (81-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Sequences, series, summability (40-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 Numerical analysis (65-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 80 Publications have been cited 1,620 times in 1,046 Documents Cited by ▼ Year ▼ Convergent sequences of dense graphs. I: Subgraph frequencies, metric properties and testing. Zbl 1213.05161 Borgs, C.; Chayes, J. T.; Lovász, L.; Sós, V. T.; Vesztergombi, K. 230 2008 Convergent sequences of dense graphs. II. Multiway cuts and statistical physics. Zbl 1247.05124 Borgs, Christian; Chayes, Jennifer T.; Lovász, László; Sós, Vera T.; Vesztergombi, Katalin 114 2012 Counting graph homomorphisms. Zbl 1129.05050 Borgs, Christian; Chayes, Jennifer; Lovász, László; Sós, Vera T.; Vesztergombi, Katalin 72 2006 Directed scale-free graphs. Zbl 1094.68605 Bollobás, Béla; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver 70 2003 Moments of two-variable functions and the uniqueness of graph limits. Zbl 1223.05193 Borgs, Christian; Chayes, Jennifer; Lovász, László 61 2010 On the spread of viruses on the Internet. Zbl 1297.68029 Berger, Noam; Borgs, Christian; Chayes, Jennifer T.; Saberi, Amin 55 2005 An \(L^p\) theory of sparse graph convergence. I: Limits, sparse random graph models, and power law distributions. Zbl 1417.05186 Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Zhao, Yufei 55 2019 Maximizing social influence in nearly optimal time. Zbl 1420.68248 Borgs, Christian; Brautbar, Michael; Chayes, Jennifer; Lucier, Brendan 51 2014 The scaling window of the 2-SAT transition. Zbl 0979.68053 Bollobás, Béla; Borgs, Christian; Chayes, Jennifer T.; Kim, Jeong Han; Wilson, David B. 47 2001 An \(L^{p}\) theory of sparse graph convergence. II: LD convergence, quotients and right convergence. Zbl 1386.05099 Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Zhao, Yufei 44 2018 Graph limits and parameter testing. Zbl 1301.68199 Borgs, Christian; Chayes, Jennifer; Lovász, László; Sós, Vera T.; Szegedy, Balázs; Vesztergombi, Katalin 44 2006 Left and right convergence of graphs with bounded degree. Zbl 1257.05172 Borgs, Christian; Chayes, Jennifer; Kahn, Jeff; Lovász, László 43 2013 Random subgraphs of finite graphs. I: The scaling window under the triangle condition. Zbl 1076.05071 Borgs, Christian; Chayes, Jennifer T.; van der Hofstad, Remco; Slade, Gordon; Spencer, Joel 40 2005 Random subgraphs of finite graphs. II: The lace expansion and the triangle condition. Zbl 1079.05087 Borgs, Christian; Chayes, Jennifer T.; van der Hofstad, Remco; Slade, Gordon; Spencer, Joel 39 2005 A unified approach to phase diagrams in field theory and statistical mechanics. Zbl 0668.60092 Borgs, Christian; Imbrie, John Z. 38 1989 Sparse exchangeable graphs and their limits via graphon processes. Zbl 1469.60158 Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Holden, Nina 38 2018 The birth of the infinite cluster: Finite-size scaling in percolation. Zbl 1038.82035 Borgs, C.; Chayes, J. T.; Kesten, H.; Spencer, J. 34 2001 Asymptotic behavior and distributional limits of preferential attachment graphs. Zbl 1296.60010 Berger, Noam; Borgs, Christian; Chayes, Jennifer T.; Saberi, Amin 33 2014 Random subgraphs of finite graphs. III: The phase transition for the \(n\)-cube. Zbl 1121.05108 Borgs, Christian; Chayes, Jennifer T.; van der Hofstad, Remco; Slade, Gordon; Spencer, Joel 27 2006 Limits of randomly grown graph sequences. Zbl 1229.05247 Borgs, Christian; Chayes, Jennifer; Lovász, László; Sós, Vera; Vesztergombi, Katalin 27 2011 Entropy-SGD: biasing gradient descent into wide valleys. Zbl 1459.65091 Chaudhari, Pratik; Choromanska, Anna; Soatto, Stefano; LeCun, Yann; Baldassi, Carlo; Borgs, Christian; Chayes, Jennifer; Sagun, Levent; Zecchina, Riccardo 26 2019 Tight bounds for mixing of the Swendsen-Wang algorithm at the Potts transition point. Zbl 1250.60034 Borgs, Christian; Chayes, Jennifer T.; Tetali, Prasad 24 2012 Low temperature phase diagrams for quantum perturbations of classical spin systems. Zbl 0858.60097 Borgs, C.; Kotecký, R.; Ueltschi, D. 21 1996 Uniform boundedness of critical crossing probabilities implies hyperscaling. Zbl 0940.60089 Borgs, C.; Chayes, J. T.; Kesten, H.; Spencer, J. 20 1999 First to market is not everything: an analysis of preferential attachment with fitness. Zbl 1232.68018 Borgs, Christian; Chayes, Jennifer 18 2007 Partition function zeros at first-order phase transitions: a general analysis. Zbl 1088.82010 Biskup, M.; Borgs, C.; Chayes, J. T.; Kleinwaks, L. J.; Kotecký, R. 18 2004 Gibbs states of graphical representations of the Potts model with external fields. Zbl 0977.82012 Biskup, M.; Borgs, C.; Chayes, J. T.; Kotecký, R. 16 2000 Partition function zeros at first-order phase transitions: Pirogov-Sinai theory. Zbl 1142.82328 Biskup, M.; Borgs, C.; Chayes, J. T.; Kotecký, R. 15 2004 Absence of zeros for the chromatic polynomial on bounded degree graphs. Zbl 1082.05034 Borgs, Christian 15 2006 Percolation on dense graph sequences. Zbl 1190.60090 Bollobás, Béla; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver 15 2010 How to distribute antidote to control epidemics. Zbl 1247.05247 Borgs, Christian; Chayes, Jennifer; Ganesh, Ayalvadi; Saberi, Amin 14 2010 Efficient sampling and counting algorithms for the Potts model on \(\mathbb{Z}^d\) at all temperatures. Zbl 07298284 Borgs, Christian; Chayes, Jennifer; Helmuth, Tyler; Perkins, Will; Tetali, Prasad 12 2020 Degree distribution of the FKP network model. Zbl 1039.68510 Berger, Noam; Bollobás, Béla; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver 11 2003 Special issue: Probabilistic techniques in equilibrium and nonequilibrium statistical physics. Zbl 0969.00035 11 2000 Bargaining dynamics in exchange networks. Zbl 1314.91112 Bayati, Mohsen; Borgs, Christian; Chayes, Jennifer; Kanoria, Yash; Montanari, Andrea 11 2015 Phase transition and finite-size scaling for the integer partitioning problem. Zbl 1014.05009 Borgs, Christian; Chayes, Jennifer; Pittel, Boris 10 2001 Sampling perspectives on sparse exchangeable graphs. Zbl 1448.60025 Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Veitch, Victor 10 2019 Belief propagation for weighted b-matchings on arbitrary graphs and its relation to linear programs with integer solutions. Zbl 1225.68130 Bayati, Mohsen; Borgs, Christian; Chayes, Jennifer; Zecchina, Riccardo 10 2011 The covariance matrix of the Potts model: a random cluster analysis. Zbl 1042.82510 Borgs, C.; Chayes, J. T. 9 1996 The van den Berg-Kesten-Reimer inequality: a review. Zbl 1115.82320 Borgs, C.; Chayes, J. T.; Randall, D. 8 1999 Consistent nonparametric estimation for heavy-tailed sparse graphs. Zbl 1486.62080 Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Ganguly, Shirshendu 8 2021 The myth of the folk theorem. Zbl 1207.91012 Borgs, Christian; Chayes, Jennifer; Immorlica, Nicole; Kalai, Adam Tauman; Mirrokni, Vahab; Papadimitriou, Christos 8 2010 A sublinear time algorithm for PageRank computations. Zbl 1342.05181 Borgs, Christian; Brautbar, Michael; Chayes, Jennifer; Teng, Shang-Hua 8 2012 Proof of the local REM conjecture for number partitioning. I: Constant energy scales. Zbl 1160.05303 Borgs, Christian; Chayes, Jennifer; Mertens, Stephan; Nair, Chandra 7 2009 Proof of the local REM conjecture for number partitioning. II. Growing energy scales. Zbl 1160.05304 Borgs, Christian; Chayes, Jennifer; Mertens, Stephan; Nair, Chandra 7 2009 Phase diagram for the constrained integer partitioning problem. Zbl 1049.90073 Borgs, C.; Chayes, J. T.; Mertens, S.; Pittel, B. 7 2004 Fast convergence of natural bargaining dynamics in exchange networks. Zbl 1377.91106 Kanoria, Yashodhan; Bayati, Mohsen; Borgs, Christian; Chayes, Jennifer; Montanari, Andrea 7 2011 Surface-induced finite-size effects for first-order phase transitions. Zbl 1081.82517 Borgs, C.; Kotecký, R. 6 1995 On the sampling problem for \(H\)-colorings on the hypercube lattice. Zbl 1074.05032 Borgs, Christian; Chayes, Jennifer T.; Dyer, Martin; Tetali, Prasad 6 2004 Local computation of pagerank contributions. Zbl 1206.68346 Andersen, Reid; Borgs, Christian; Chayes, Jennifer; Hopcroft, John; Mirrokni, Vahab; Teng, Shang-Hua 6 2008 First order phase transitions in unbounded spin systems. II: Completeness of the phase diagram. Zbl 0719.60121 Borgs, Christian; Waxler, Roger 6 1990 The myth of the folk theorem. Zbl 1231.91006 Borgs, Christian; Chayes, Jennifer; Immorlica, Nicole; Kalai, Adam Tauman; Mirrokni, Vahab; Papadimitriou, Christos 5 2008 Mean-field lattice trees. Zbl 0934.60089 Borgs, Christian; Chayes, Jennifer; van der Hofstad, Remco; Slade, Gordon 5 1999 Competition-induced preferential attachment. Zbl 1098.68009 Berger, N.; Borgs, C.; Chayes, J. T.; D’Souza, R. M.; Kleinberg, R. D. 5 2004 Multiscale matrix sampling and sublinear-time PageRank computation. Zbl 1462.68008 Borgs, Christian; Brautbar, Michael; Chayes, Jennifer; Teng, Shang-Hua 5 2014 Convergent sequences of sparse graphs: a large deviations approach. Zbl 1370.05119 Borgs, Christian; Chayes, Jennifer; Gamarnik, David 5 2017 The optimal admission threshold in observable queues with state dependent pricing. Zbl 1302.90042 Borgs, Christian; Chayes, Jennifer T.; Doroudi, Sherwin; Harchol-Balter, Mor; Xu, Kuang 5 2014 First order phase transitions in unbounded spin systems. I: Construction of the phase diagram. Zbl 0689.60088 Borgs, Christian; Waxler, Roger 5 1989 Finite-size scaling and surface tension from effective one dimensional systems. Zbl 0754.60129 Borgs, Christian; Imbrie, John Z. 5 1992 Local computation of PageRank contributions. Zbl 1136.68316 Andersen, Reid; Borgs, Christian; Chayes, Jennifer; Hopcraft, John; Mirrokni, Vahab S.; Teng, Shang-Hua 4 2007 Degree distribution of competition-induced preferential attachment graphs. Zbl 1087.05050 Berger, N.; Borgs, C.; Chayes, J. T.; D’Souza, R. M.; Kleinberg, R. D. 4 2005 Finding endogenously formed communities. Zbl 1422.68203 Balcan, Maria-Florina; Borgs, Christian; Braverman, Mark; Chayes, Jennifer; Teng, Shang-Hua 3 2013 The staggered charge-order phase of the extended Hubbard model in the atomic limit. Zbl 0946.81523 Borgs, Christian; Jędrzejewski, Janusz; Kotecký, Roman 3 1996 Finite-size effects for the Potts model with weak boundary conditions. Zbl 1027.82008 Borgs, C.; Kotecký, R.; Medved’, I. 3 2002 Symmetry breaking in Landau gauge. A comment to a paper by T. Kennedy and C. King. Zbl 0593.46062 Borgs, Christian; Nill, Florian 3 1986 Limits of sparse configuration models and beyond: graphexes and multigraphexes. Zbl 1481.05138 Borgs, Christian; Chayes, Jennifer T.; Dhara, Souvik; Sen, Subhabrata 3 2021 Confinement, deconfinement and freezing in lattice Yang-Mills theories with continuous time. Zbl 1223.81145 Borgs, Christian 3 1988 Sharp threshold and scaling window for the integer partitioning problem. Zbl 1323.68311 Borgs, Christian; Chayes, Jennifer; Pittel, Boris 3 2001 Identifiability for graphexes and the weak kernel metric. Zbl 1443.05169 Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Lovász, László Miklós 3 2019 Dobrushin states in quantum lattice systems. Zbl 0888.60093 Borgs, C.; Chayes, J. T.; Fröhlich, J. 2 1997 Crossover finite-size scaling at first-order transitions. Zbl 0893.60075 Borgs, Christian; Imbrie, John Z. 2 1992 Degree distribution of the FKP network model. Zbl 1149.90030 Berger, Noam; Bollobás, Béla; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver 2 2007 Low temperature phase diagrams of fermionic lattice systems. Zbl 0979.82004 Borgs, C.; Kotecký, R. 2 2000 An axiomatic approach to community detection. Zbl 1334.91061 Borgs, Christian; Chayes, Jennifer; Marple, Adrian; Teng, Shang-Hua 2 2016 Dobrushin states for classical spin systems with complex interactions. Zbl 0945.82516 Borgs, C.; Chayes, J. T.; Fröhlich, J. 1 1997 Meissner phase for a model of oriented flux lines. Zbl 0877.60067 Borgs, C.; Chayes, J. T.; King, C. 1 1995 Finite-size scaling of the mass-gap for first-order phase transitions. Zbl 0989.82509 Borgs, Christian 1 1993 Anisotropic self-avoiding walks. Zbl 1052.82013 Borgs, Christian; Chayes, Jennifer; King, Christopher; Madras, Neal 1 2000 Iterative collaborative filtering for sparse matrix estimation. Zbl 07640288 Borgs, Christian; Chayes, Jennifer T.; Shah, Devavrat; Yu, Christina Lee 1 2022 Game-theoretic models of information overload in social networks. Zbl 1310.91034 Borgs, Christian; Chayes, Jennifer; Karrer, Brian; Meeder, Brendan; Ravi, R.; Reagans, Ray; Sayedi, Amin 1 2010 Iterative collaborative filtering for sparse matrix estimation. Zbl 07640288 Borgs, Christian; Chayes, Jennifer T.; Shah, Devavrat; Yu, Christina Lee 1 2022 Consistent nonparametric estimation for heavy-tailed sparse graphs. Zbl 1486.62080 Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Ganguly, Shirshendu 8 2021 Limits of sparse configuration models and beyond: graphexes and multigraphexes. Zbl 1481.05138 Borgs, Christian; Chayes, Jennifer T.; Dhara, Souvik; Sen, Subhabrata 3 2021 Efficient sampling and counting algorithms for the Potts model on \(\mathbb{Z}^d\) at all temperatures. Zbl 07298284 Borgs, Christian; Chayes, Jennifer; Helmuth, Tyler; Perkins, Will; Tetali, Prasad 12 2020 An \(L^p\) theory of sparse graph convergence. I: Limits, sparse random graph models, and power law distributions. Zbl 1417.05186 Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Zhao, Yufei 55 2019 Entropy-SGD: biasing gradient descent into wide valleys. Zbl 1459.65091 Chaudhari, Pratik; Choromanska, Anna; Soatto, Stefano; LeCun, Yann; Baldassi, Carlo; Borgs, Christian; Chayes, Jennifer; Sagun, Levent; Zecchina, Riccardo 26 2019 Sampling perspectives on sparse exchangeable graphs. Zbl 1448.60025 Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Veitch, Victor 10 2019 Identifiability for graphexes and the weak kernel metric. Zbl 1443.05169 Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Lovász, László Miklós 3 2019 An \(L^{p}\) theory of sparse graph convergence. II: LD convergence, quotients and right convergence. Zbl 1386.05099 Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Zhao, Yufei 44 2018 Sparse exchangeable graphs and their limits via graphon processes. Zbl 1469.60158 Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Holden, Nina 38 2018 Convergent sequences of sparse graphs: a large deviations approach. Zbl 1370.05119 Borgs, Christian; Chayes, Jennifer; Gamarnik, David 5 2017 An axiomatic approach to community detection. Zbl 1334.91061 Borgs, Christian; Chayes, Jennifer; Marple, Adrian; Teng, Shang-Hua 2 2016 Bargaining dynamics in exchange networks. Zbl 1314.91112 Bayati, Mohsen; Borgs, Christian; Chayes, Jennifer; Kanoria, Yash; Montanari, Andrea 11 2015 Maximizing social influence in nearly optimal time. Zbl 1420.68248 Borgs, Christian; Brautbar, Michael; Chayes, Jennifer; Lucier, Brendan 51 2014 Asymptotic behavior and distributional limits of preferential attachment graphs. Zbl 1296.60010 Berger, Noam; Borgs, Christian; Chayes, Jennifer T.; Saberi, Amin 33 2014 Multiscale matrix sampling and sublinear-time PageRank computation. Zbl 1462.68008 Borgs, Christian; Brautbar, Michael; Chayes, Jennifer; Teng, Shang-Hua 5 2014 The optimal admission threshold in observable queues with state dependent pricing. Zbl 1302.90042 Borgs, Christian; Chayes, Jennifer T.; Doroudi, Sherwin; Harchol-Balter, Mor; Xu, Kuang 5 2014 Left and right convergence of graphs with bounded degree. Zbl 1257.05172 Borgs, Christian; Chayes, Jennifer; Kahn, Jeff; Lovász, László 43 2013 Finding endogenously formed communities. Zbl 1422.68203 Balcan, Maria-Florina; Borgs, Christian; Braverman, Mark; Chayes, Jennifer; Teng, Shang-Hua 3 2013 Convergent sequences of dense graphs. II. Multiway cuts and statistical physics. Zbl 1247.05124 Borgs, Christian; Chayes, Jennifer T.; Lovász, László; Sós, Vera T.; Vesztergombi, Katalin 114 2012 Tight bounds for mixing of the Swendsen-Wang algorithm at the Potts transition point. Zbl 1250.60034 Borgs, Christian; Chayes, Jennifer T.; Tetali, Prasad 24 2012 A sublinear time algorithm for PageRank computations. Zbl 1342.05181 Borgs, Christian; Brautbar, Michael; Chayes, Jennifer; Teng, Shang-Hua 8 2012 Limits of randomly grown graph sequences. Zbl 1229.05247 Borgs, Christian; Chayes, Jennifer; Lovász, László; Sós, Vera; Vesztergombi, Katalin 27 2011 Belief propagation for weighted b-matchings on arbitrary graphs and its relation to linear programs with integer solutions. Zbl 1225.68130 Bayati, Mohsen; Borgs, Christian; Chayes, Jennifer; Zecchina, Riccardo 10 2011 Fast convergence of natural bargaining dynamics in exchange networks. Zbl 1377.91106 Kanoria, Yashodhan; Bayati, Mohsen; Borgs, Christian; Chayes, Jennifer; Montanari, Andrea 7 2011 Moments of two-variable functions and the uniqueness of graph limits. Zbl 1223.05193 Borgs, Christian; Chayes, Jennifer; Lovász, László 61 2010 Percolation on dense graph sequences. Zbl 1190.60090 Bollobás, Béla; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver 15 2010 How to distribute antidote to control epidemics. Zbl 1247.05247 Borgs, Christian; Chayes, Jennifer; Ganesh, Ayalvadi; Saberi, Amin 14 2010 The myth of the folk theorem. Zbl 1207.91012 Borgs, Christian; Chayes, Jennifer; Immorlica, Nicole; Kalai, Adam Tauman; Mirrokni, Vahab; Papadimitriou, Christos 8 2010 Game-theoretic models of information overload in social networks. Zbl 1310.91034 Borgs, Christian; Chayes, Jennifer; Karrer, Brian; Meeder, Brendan; Ravi, R.; Reagans, Ray; Sayedi, Amin 1 2010 Proof of the local REM conjecture for number partitioning. I: Constant energy scales. Zbl 1160.05303 Borgs, Christian; Chayes, Jennifer; Mertens, Stephan; Nair, Chandra 7 2009 Proof of the local REM conjecture for number partitioning. II. Growing energy scales. Zbl 1160.05304 Borgs, Christian; Chayes, Jennifer; Mertens, Stephan; Nair, Chandra 7 2009 Convergent sequences of dense graphs. I: Subgraph frequencies, metric properties and testing. Zbl 1213.05161 Borgs, C.; Chayes, J. T.; Lovász, L.; Sós, V. T.; Vesztergombi, K. 230 2008 Local computation of pagerank contributions. Zbl 1206.68346 Andersen, Reid; Borgs, Christian; Chayes, Jennifer; Hopcroft, John; Mirrokni, Vahab; Teng, Shang-Hua 6 2008 The myth of the folk theorem. Zbl 1231.91006 Borgs, Christian; Chayes, Jennifer; Immorlica, Nicole; Kalai, Adam Tauman; Mirrokni, Vahab; Papadimitriou, Christos 5 2008 First to market is not everything: an analysis of preferential attachment with fitness. Zbl 1232.68018 Borgs, Christian; Chayes, Jennifer 18 2007 Local computation of PageRank contributions. Zbl 1136.68316 Andersen, Reid; Borgs, Christian; Chayes, Jennifer; Hopcraft, John; Mirrokni, Vahab S.; Teng, Shang-Hua 4 2007 Degree distribution of the FKP network model. Zbl 1149.90030 Berger, Noam; Bollobás, Béla; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver 2 2007 Counting graph homomorphisms. Zbl 1129.05050 Borgs, Christian; Chayes, Jennifer; Lovász, László; Sós, Vera T.; Vesztergombi, Katalin 72 2006 Graph limits and parameter testing. Zbl 1301.68199 Borgs, Christian; Chayes, Jennifer; Lovász, László; Sós, Vera T.; Szegedy, Balázs; Vesztergombi, Katalin 44 2006 Random subgraphs of finite graphs. III: The phase transition for the \(n\)-cube. Zbl 1121.05108 Borgs, Christian; Chayes, Jennifer T.; van der Hofstad, Remco; Slade, Gordon; Spencer, Joel 27 2006 Absence of zeros for the chromatic polynomial on bounded degree graphs. Zbl 1082.05034 Borgs, Christian 15 2006 On the spread of viruses on the Internet. Zbl 1297.68029 Berger, Noam; Borgs, Christian; Chayes, Jennifer T.; Saberi, Amin 55 2005 Random subgraphs of finite graphs. I: The scaling window under the triangle condition. Zbl 1076.05071 Borgs, Christian; Chayes, Jennifer T.; van der Hofstad, Remco; Slade, Gordon; Spencer, Joel 40 2005 Random subgraphs of finite graphs. II: The lace expansion and the triangle condition. Zbl 1079.05087 Borgs, Christian; Chayes, Jennifer T.; van der Hofstad, Remco; Slade, Gordon; Spencer, Joel 39 2005 Degree distribution of competition-induced preferential attachment graphs. Zbl 1087.05050 Berger, N.; Borgs, C.; Chayes, J. T.; D’Souza, R. M.; Kleinberg, R. D. 4 2005 Partition function zeros at first-order phase transitions: a general analysis. Zbl 1088.82010 Biskup, M.; Borgs, C.; Chayes, J. T.; Kleinwaks, L. J.; Kotecký, R. 18 2004 Partition function zeros at first-order phase transitions: Pirogov-Sinai theory. Zbl 1142.82328 Biskup, M.; Borgs, C.; Chayes, J. T.; Kotecký, R. 15 2004 Phase diagram for the constrained integer partitioning problem. Zbl 1049.90073 Borgs, C.; Chayes, J. T.; Mertens, S.; Pittel, B. 7 2004 On the sampling problem for \(H\)-colorings on the hypercube lattice. Zbl 1074.05032 Borgs, Christian; Chayes, Jennifer T.; Dyer, Martin; Tetali, Prasad 6 2004 Competition-induced preferential attachment. Zbl 1098.68009 Berger, N.; Borgs, C.; Chayes, J. T.; D’Souza, R. M.; Kleinberg, R. D. 5 2004 Directed scale-free graphs. Zbl 1094.68605 Bollobás, Béla; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver 70 2003 Degree distribution of the FKP network model. Zbl 1039.68510 Berger, Noam; Bollobás, Béla; Borgs, Christian; Chayes, Jennifer; Riordan, Oliver 11 2003 Finite-size effects for the Potts model with weak boundary conditions. Zbl 1027.82008 Borgs, C.; Kotecký, R.; Medved’, I. 3 2002 The scaling window of the 2-SAT transition. Zbl 0979.68053 Bollobás, Béla; Borgs, Christian; Chayes, Jennifer T.; Kim, Jeong Han; Wilson, David B. 47 2001 The birth of the infinite cluster: Finite-size scaling in percolation. Zbl 1038.82035 Borgs, C.; Chayes, J. T.; Kesten, H.; Spencer, J. 34 2001 Phase transition and finite-size scaling for the integer partitioning problem. Zbl 1014.05009 Borgs, Christian; Chayes, Jennifer; Pittel, Boris 10 2001 Sharp threshold and scaling window for the integer partitioning problem. Zbl 1323.68311 Borgs, Christian; Chayes, Jennifer; Pittel, Boris 3 2001 Gibbs states of graphical representations of the Potts model with external fields. Zbl 0977.82012 Biskup, M.; Borgs, C.; Chayes, J. T.; Kotecký, R. 16 2000 Special issue: Probabilistic techniques in equilibrium and nonequilibrium statistical physics. Zbl 0969.00035 11 2000 Low temperature phase diagrams of fermionic lattice systems. Zbl 0979.82004 Borgs, C.; Kotecký, R. 2 2000 Anisotropic self-avoiding walks. Zbl 1052.82013 Borgs, Christian; Chayes, Jennifer; King, Christopher; Madras, Neal 1 2000 Uniform boundedness of critical crossing probabilities implies hyperscaling. Zbl 0940.60089 Borgs, C.; Chayes, J. T.; Kesten, H.; Spencer, J. 20 1999 The van den Berg-Kesten-Reimer inequality: a review. Zbl 1115.82320 Borgs, C.; Chayes, J. T.; Randall, D. 8 1999 Mean-field lattice trees. Zbl 0934.60089 Borgs, Christian; Chayes, Jennifer; van der Hofstad, Remco; Slade, Gordon 5 1999 Dobrushin states in quantum lattice systems. Zbl 0888.60093 Borgs, C.; Chayes, J. T.; Fröhlich, J. 2 1997 Dobrushin states for classical spin systems with complex interactions. Zbl 0945.82516 Borgs, C.; Chayes, J. T.; Fröhlich, J. 1 1997 Low temperature phase diagrams for quantum perturbations of classical spin systems. Zbl 0858.60097 Borgs, C.; Kotecký, R.; Ueltschi, D. 21 1996 The covariance matrix of the Potts model: a random cluster analysis. Zbl 1042.82510 Borgs, C.; Chayes, J. T. 9 1996 The staggered charge-order phase of the extended Hubbard model in the atomic limit. Zbl 0946.81523 Borgs, Christian; Jędrzejewski, Janusz; Kotecký, Roman 3 1996 Surface-induced finite-size effects for first-order phase transitions. Zbl 1081.82517 Borgs, C.; Kotecký, R. 6 1995 Meissner phase for a model of oriented flux lines. Zbl 0877.60067 Borgs, C.; Chayes, J. T.; King, C. 1 1995 Finite-size scaling of the mass-gap for first-order phase transitions. Zbl 0989.82509 Borgs, Christian 1 1993 Finite-size scaling and surface tension from effective one dimensional systems. Zbl 0754.60129 Borgs, Christian; Imbrie, John Z. 5 1992 Crossover finite-size scaling at first-order transitions. Zbl 0893.60075 Borgs, Christian; Imbrie, John Z. 2 1992 First order phase transitions in unbounded spin systems. II: Completeness of the phase diagram. Zbl 0719.60121 Borgs, Christian; Waxler, Roger 6 1990 A unified approach to phase diagrams in field theory and statistical mechanics. Zbl 0668.60092 Borgs, Christian; Imbrie, John Z. 38 1989 First order phase transitions in unbounded spin systems. I: Construction of the phase diagram. Zbl 0689.60088 Borgs, Christian; Waxler, Roger 5 1989 Confinement, deconfinement and freezing in lattice Yang-Mills theories with continuous time. Zbl 1223.81145 Borgs, Christian 3 1988 Symmetry breaking in Landau gauge. A comment to a paper by T. Kennedy and C. King. Zbl 0593.46062 Borgs, Christian; Nill, Florian 3 1986 all cited Publications top 5 cited Publications all top 5 Cited by 1,552 Authors 38 Borgs, Christian 32 van der Hofstad, Remco W. 29 Chayes, Jennifer Tour 19 Janson, Svante 19 Lovász, László 16 Nešetřil, Jaroslav 15 Král’, Daniel 15 Zhao, Yufei 14 Hladký, Jan 13 Regts, Guus 13 Resnick, Sidney Ira 13 Szegedy, Balázs 12 Nachmias, Asaf 11 Bollobás, Béla 11 Wang, Tiandong 10 Biskup, Marek 10 Shojaei-Fard, Ali 10 Sly, Allan 9 Hoppen, Carlos 9 Perkins, Will 8 Chayes, Lincoln 8 Fox, Jacob 8 Heydenreich, Markus 8 Kohayakawa, Yoshiharu 8 Medvedev, Georgi S. 8 Riordan, Oliver Maxim 8 Slade, Gordon 8 Vigoda, Eric 7 Bhattacharya, Bhaswar B. 7 Csikvári, Péter 7 den Hollander, Frank 7 Gheissari, Reza 7 Kotecký, Roman 7 Lovász, László Miklós 7 Lubetzky, Eyal 7 Ossona de Mendez, Patrice 7 Peres, Yuval 7 Pikhurko, Oleg 7 Pittel, Boris G. 7 Röllin, Adrian 6 Blanca, Antonio 6 Bolla, Marianna 6 Camia, Federico 6 Chatterjee, Sourav 6 Chung, Fan 6 Cohn, Henry Lee 6 Das, Bikramjit 6 Dembo, Amir 6 Ding, Jian 6 Doležal, Martin 6 Goldberg, Leslie Ann 6 Jordan, Jonathan H. 6 Mukherjee, Sumit 6 Nolin, Pierre 6 Radin, Charles 6 Sinclair, Alistair 6 Sun, Nike 6 Wu, Weili 6 Yin, Mei 5 Backhausz, Ágnes M. 5 Bhamidi, Shankar 5 Diaconis, Persi Warren 5 Duminil-Copin, Hugo 5 Durrett, Richard Timothy 5 Fernández, Roberto 5 Fröhlich, Jürg Martin 5 Galanis, Andreas 5 Garijo, Delia 5 Glebov, Roman 5 Goodall, Andrew J. 5 Helmuth, Tyler 5 Hooghiemstra, Gerard 5 Janssen, Jeannette C. M. 5 Kozma, Gady 5 Kunszenti-Kovács, Dávid 5 Li, Deying 5 Manolescu, Ioan 5 Patel, Viresh 5 Sadun, Lorenzo A. 5 Sampaio, Rudini Menezes 5 Sivakoff, David J. 5 Sós, Vera Turán 5 Sudan, Madhu 5 Ueltschi, Daniel 5 Wade, Andrew R. 4 Bodineau, Thierry 4 Braides, Andrea 4 Bressan, Marco 4 Caputo, Pietro 4 Chatterjee, Shirshendu 4 Chen, Shengminjie 4 Chen, Wenping 4 D’Angelo, Gianlorenzo 4 Dhara, Souvik 4 Du, Ding-Zhu 4 Elek, Gábor 4 Elmoataz, Abderrahim 4 Fadili, Jalal M. 4 Garavaglia, Alessandro 4 Ghandehari, Mahya ...and 1,452 more Authors all top 5 Cited in 227 Serials 65 Journal of Statistical Physics 57 Random Structures & Algorithms 44 Communications in Mathematical Physics 36 European Journal of Combinatorics 35 The Annals of Applied Probability 31 The Annals of Probability 31 Probability Theory and Related Fields 30 Theoretical Computer Science 27 Combinatorics, Probability and Computing 15 Journal of Applied Probability 15 Stochastic Processes and their Applications 14 The Annals of Statistics 14 Journal of Statistical Mechanics: Theory and Experiment 13 Advances in Applied Probability 13 Journal of Mathematical Physics 13 Advances in Mathematics 13 Journal of Combinatorial Theory. Series B 13 Electronic Journal of Probability 12 SIAM Journal on Discrete Mathematics 10 Discrete Mathematics 10 Algorithmica 9 Information Sciences 9 Combinatorica 8 Artificial Intelligence 8 Discrete Applied Mathematics 8 Journal of Graph Theory 8 Journal of Machine Learning Research (JMLR) 7 Operations Research 7 Transactions of the American Mathematical Society 7 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 7 Bernoulli 7 Internet Mathematics 6 Israel Journal of Mathematics 6 Physica A 6 Computational Complexity 6 The Electronic Journal of Combinatorics 6 Electronic Communications in Probability 6 Journal of Combinatorial Optimization 6 Extremes 6 Oberwolfach Reports 6 Electronic Journal of Statistics 5 Reviews in Mathematical Physics 5 Applied Mathematics and Computation 5 SIAM Journal on Computing 5 Geometric and Functional Analysis. GAFA 5 Methodology and Computing in Applied Probability 5 Computer Science Review 4 Nuclear Physics. B 4 Journal of Computer and System Sciences 4 Journal of Economic Theory 4 SIAM Journal on Control and Optimization 4 Acta Mathematica Hungarica 4 Statistical Science 4 Machine Learning 4 Theory of Computing Systems 4 Annals of Mathematics. Second Series 4 ALEA. Latin American Journal of Probability and Mathematical Statistics 4 Statistics and Computing 3 Communications on Pure and Applied Mathematics 3 Physics Reports 3 Applied Mathematics and Optimization 3 Inventiones Mathematicae 3 Journal of Combinatorial Theory. Series A 3 Journal of Functional Analysis 3 Proceedings of the American Mathematical Society 3 Advances in Applied Mathematics 3 Journal of Theoretical Probability 3 Journal of the American Mathematical Society 3 Games and Economic Behavior 3 Linear Algebra and its Applications 3 Proceedings of the National Academy of Sciences of the United States of America 3 Journal of Nonlinear Science 3 Complexity 3 Mathematical Physics, Analysis and Geometry 3 Chaos 3 Journal of High Energy Physics 3 Journal of Physics A: Mathematical and Theoretical 3 Discrete Analysis 3 SIAM Journal on Mathematics of Data Science 2 Archive for Rational Mechanics and Analysis 2 Information Processing Letters 2 Journal of Mathematical Analysis and Applications 2 Rocky Mountain Journal of Mathematics 2 Chaos, Solitons and Fractals 2 International Journal of Game Theory 2 Journal of Algebra 2 Journal of the American Statistical Association 2 Journal of Differential Equations 2 Journal of Multivariate Analysis 2 Mathematics of Operations Research 2 Networks 2 SIAM Journal on Numerical Analysis 2 Physica D 2 Information and Computation 2 Asia-Pacific Journal of Operational Research 2 Annals of Physics 2 SIAM Journal on Applied Mathematics 2 SIAM Journal on Mathematical Analysis 2 Bulletin of the American Mathematical Society. New Series 2 Mathematical Programming. Series A. Series B ...and 127 more Serials all top 5 Cited in 53 Fields 552 Combinatorics (05-XX) 374 Probability theory and stochastic processes (60-XX) 276 Statistical mechanics, structure of matter (82-XX) 207 Computer science (68-XX) 107 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 88 Operations research, mathematical programming (90-XX) 67 Statistics (62-XX) 48 Quantum theory (81-XX) 42 Biology and other natural sciences (92-XX) 21 Numerical analysis (65-XX) 19 Functional analysis (46-XX) 18 Dynamical systems and ergodic theory (37-XX) 17 Partial differential equations (35-XX) 13 Mathematical logic and foundations (03-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 13 Measure and integration (28-XX) 13 Information and communication theory, circuits (94-XX) 11 Ordinary differential equations (34-XX) 11 Systems theory; control (93-XX) 9 Number theory (11-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 8 General and overarching topics; collections (00-XX) 8 Order, lattices, ordered algebraic structures (06-XX) 5 Functions of a complex variable (30-XX) 5 Approximations and expansions (41-XX) 5 Integral equations (45-XX) 5 Operator theory (47-XX) 5 Convex and discrete geometry (52-XX) 5 General topology (54-XX) 5 Mechanics of deformable solids (74-XX) 4 History and biography (01-XX) 4 Group theory and generalizations (20-XX) 4 Mechanics of particles and systems (70-XX) 3 General algebraic systems (08-XX) 3 Algebraic geometry (14-XX) 3 Associative rings and algebras (16-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Special functions (33-XX) 2 Abstract harmonic analysis (43-XX) 2 Integral transforms, operational calculus (44-XX) 2 Differential geometry (53-XX) 1 Field theory and polynomials (12-XX) 1 Category theory; homological algebra (18-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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