Xi, Mengmei; Wang, Chunhua; Wang, Xuejun Uniformly strong consistency and the rates of asymptotic normality for the edge frequency polygons. (English) Zbl 07803286 Statistics 57, No. 6, 1444-1468 (2023). MSC: 62G20 62G07 60E05 PDFBibTeX XMLCite \textit{M. Xi} et al., Statistics 57, No. 6, 1444--1468 (2023; Zbl 07803286) Full Text: DOI
Gusakova, Anna; Reitzner, Matthias; Thäle, Christoph Variance expansion and Berry-Esseen bound for the number of vertices of a random polygon in a polygon. (Asymptotique de la variance et bornes de Berry-Esseen pour le nombre de sommets d’un polygone aléatoire dans un polygone.) (English. French summary) Zbl 1523.52008 Ann. Henri Lebesgue 6, 875-906 (2023). MSC: 52A22 60D05 PDFBibTeX XMLCite \textit{A. Gusakova} et al., Ann. Henri Lebesgue 6, 875--906 (2023; Zbl 1523.52008) Full Text: DOI arXiv
Fodor, Ferenc; Kevei, Péter; Vígh, Viktor On random disc-polygons in a disc-polygon. (English) Zbl 1519.52003 Electron. Commun. Probab. 28, Paper No. 10, 11 p. (2023). Reviewer: Rolf Schneider (Freiburg im Breisgau) MSC: 52A22 60D05 PDFBibTeX XMLCite \textit{F. Fodor} et al., Electron. Commun. Probab. 28, Paper No. 10, 11 p. (2023; Zbl 1519.52003) Full Text: DOI arXiv
Fodor, Ferenc; Pinzón, Nicolás A. Montenegro; Vígh, Viktor On Wendel’s equality for intersections of balls. (English) Zbl 1511.52008 Aequationes Math. 97, No. 2, 439-451 (2023). MSC: 52A22 52A27 60D05 PDFBibTeX XMLCite \textit{F. Fodor} et al., Aequationes Math. 97, No. 2, 439--451 (2023; Zbl 1511.52008) Full Text: DOI
Madras, Neal Adsorption of lattice polymers with quenched topologies. (English) Zbl 1502.82007 J. Stat. Phys. 190, No. 1, Paper No. 7, 50 p. (2023). MSC: 82B41 60K35 82D60 PDFBibTeX XMLCite \textit{N. Madras}, J. Stat. Phys. 190, No. 1, Paper No. 7, 50 p. (2023; Zbl 1502.82007) Full Text: DOI arXiv
Aliashvili, T. Topological invariants of random polynomials. (English) Zbl 07731848 Proc. I. Vekua Inst. Appl. Math. 72, 3-11 (2022). MSC: 60G99 12D10 26C10 PDFBibTeX XMLCite \textit{T. Aliashvili}, Proc. I. Vekua Inst. Appl. Math. 72, 3--11 (2022; Zbl 07731848) Full Text: Link
Chung, Incheoul; Sun, Xingping; Zheng, Songfeng Convergence of random polygon sequences. (English) Zbl 1511.52006 Involve 15, No. 4, 547-558 (2022). Reviewer: Viktor Ohanyan (Erevan) MSC: 52A22 60G20 15B52 60B20 60E05 PDFBibTeX XMLCite \textit{I. Chung} et al., Involve 15, No. 4, 547--558 (2022; Zbl 1511.52006) Full Text: DOI
Hansen, Joel; Marquez, Itzamar; Roychowdhury, Mrinal K.; Torres, Eduardo Quantization coefficients for uniform distributions on the boundaries of regular polygons. (English) Zbl 1482.60018 Stat. Probab. Lett. 173, Article ID 109060, 6 p. (2021). Reviewer: Dmitry Zaporozhets (Sankt-Peterburg) MSC: 60E05 94A34 PDFBibTeX XMLCite \textit{J. Hansen} et al., Stat. Probab. Lett. 173, Article ID 109060, 6 p. (2021; Zbl 1482.60018) Full Text: DOI arXiv
Wang, Wei; Huang, Haiwu; Wu, Yi; Chen, Kan On the uniform consistency of frequency polygons for \(\rho^-\)-mixing samples. (English) Zbl 1476.62072 J. Math. Inequal. 15, No. 3, 1287-1298 (2021). MSC: 62G07 60E15 62G20 PDFBibTeX XMLCite \textit{W. Wang} et al., J. Math. Inequal. 15, No. 3, 1287--1298 (2021; Zbl 1476.62072) Full Text: DOI
Khamdamov, Isakjan M.; Chay, Zoya S. Joint distribution of the number of vertices and the area of convex hulls generated by a uniform distribution in a convex polygon. (English) Zbl 07334160 J. Sib. Fed. Univ., Math. Phys. 14, No. 2, 230-241 (2021). MSC: 60Dxx 52Axx PDFBibTeX XMLCite \textit{I. M. Khamdamov} and \textit{Z. S. Chay}, J. Sib. Fed. Univ., Math. Phys. 14, No. 2, 230--241 (2021; Zbl 07334160) Full Text: MNR
Nikitin, Ya. Yu.; Polevaya, T. A. On the average perimeter of the inscribed random polygon. (English. Russian original) Zbl 1460.62034 Vestn. St. Petersbg. Univ., Math. 53, No. 1, 58-63 (2020); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 7(65), No. 1, 77-84 (2020). MSC: 62F10 60D05 60G60 51E12 PDFBibTeX XMLCite \textit{Ya. Yu. Nikitin} and \textit{T. A. Polevaya}, Vestn. St. Petersbg. Univ., Math. 53, No. 1, 58--63 (2020; Zbl 1460.62034); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 7(65), No. 1, 77--84 (2020) Full Text: DOI
Xu, Wen-Qing; Meng, Linlin; Li, Yong Random polygons and estimations of \(\pi\). (English) Zbl 1453.60018 Open Math. 17, 575-581 (2019). MSC: 60D05 60-08 PDFBibTeX XMLCite \textit{W.-Q. Xu} et al., Open Math. 17, 575--581 (2019; Zbl 1453.60018) Full Text: DOI
Cantarella, Jason; Chapman, Kyle; Reiter, Philipp; Shonkwiler, Clayton Open and closed random walks with fixed edgelengths in \(\mathbf{\mathbb{R}^d}\). (English) Zbl 1409.60069 J. Phys. A, Math. Theor. 51, No. 43, Article ID 434002, 24 p. (2018). MSC: 60G50 51E12 57M25 PDFBibTeX XMLCite \textit{J. Cantarella} et al., J. Phys. A, Math. Theor. 51, No. 43, Article ID 434002, 24 p. (2018; Zbl 1409.60069) Full Text: DOI arXiv
Fodor, Ferenc; Vígh, Viktor Variance estimates for random disc-polygons in smooth convex discs. (English) Zbl 1407.52004 J. Appl. Probab. 55, No. 4, 1143-1157 (2018). Reviewer: Joscha Prochno (Graz) MSC: 52A22 60D05 PDFBibTeX XMLCite \textit{F. Fodor} and \textit{V. Vígh}, J. Appl. Probab. 55, No. 4, 1143--1157 (2018; Zbl 1407.52004) Full Text: DOI arXiv Link
Hammond, Alan An upper bound on the number of self-avoiding polygons via joining. (English) Zbl 1434.60294 Ann. Probab. 46, No. 1, 175-206 (2018). MSC: 60K35 60D05 PDFBibTeX XMLCite \textit{A. Hammond}, Ann. Probab. 46, No. 1, 175--206 (2018; Zbl 1434.60294) Full Text: DOI arXiv
Grimmett, Geoffrey R.; Li, Zhongyang The 1-2 model. (English) Zbl 1390.82013 Basmajian, Ara S. (ed.) et al., In the tradition of Ahlfors-Bers, VII. Proceedings of the 6th Ahlfors-Bers colloquium, Yale University, New Haven, CT, USA, October 23–26, 2014. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2651-4/pbk; 978-1-4704-4198-2/ebook). Contemporary Mathematics 696, 139-152 (2017). MSC: 82B20 60K35 05C70 PDFBibTeX XMLCite \textit{G. R. Grimmett} and \textit{Z. Li}, Contemp. Math. 696, 139--152 (2017; Zbl 1390.82013) Full Text: DOI arXiv
Marckert, Jean-François The probability that \(n\) random points in a disk are in convex position. (English) Zbl 1372.52009 Braz. J. Probab. Stat. 31, No. 2, 320-337 (2017). Reviewer: Viktor Ohanyan (Erevan) MSC: 52A22 60D05 53C65 PDFBibTeX XMLCite \textit{J.-F. Marckert}, Braz. J. Probab. Stat. 31, No. 2, 320--337 (2017; Zbl 1372.52009) Full Text: DOI arXiv
Maehara, Hiroshi; Martini, Horst Geometric probability on the sphere. (English) Zbl 1401.60019 Jahresber. Dtsch. Math.-Ver. 119, No. 2, 93-132 (2017). Reviewer: Florian Pausinger (Belfast) MSC: 60D05 52A22 53C65 60-02 PDFBibTeX XMLCite \textit{H. Maehara} and \textit{H. Martini}, Jahresber. Dtsch. Math.-Ver. 119, No. 2, 93--132 (2017; Zbl 1401.60019) Full Text: DOI
Ye, Dandan; Dai, Meifeng; Sun, Yanqiu; Shao, Shuxiang; Xie, Qi Average receiving scaling of the weighted polygon Koch networks with the weight-dependent walk. (English) Zbl 1400.60095 Physica A 458, 1-8 (2016). MSC: 60J20 28A80 PDFBibTeX XMLCite \textit{D. Ye} et al., Physica A 458, 1--8 (2016; Zbl 1400.60095) Full Text: DOI
Grimmett, Geoffrey R.; Li, Zhongyang Critical surface of the hexagonal polygon model. (English) Zbl 1342.82032 J. Stat. Phys. 163, No. 4, 733-753 (2016). MSC: 82B20 05C10 05C70 60K35 PDFBibTeX XMLCite \textit{G. R. Grimmett} and \textit{Z. Li}, J. Stat. Phys. 163, No. 4, 733--753 (2016; Zbl 1342.82032) Full Text: DOI arXiv
Cantarella, Jason; Shonkwiler, Clayton The symplectic geometry of closed equilateral random walks in 3-space. (English) Zbl 1408.53109 Ann. Appl. Probab. 26, No. 1, 549-596 (2016). MSC: 53D30 60G50 PDFBibTeX XMLCite \textit{J. Cantarella} and \textit{C. Shonkwiler}, Ann. Appl. Probab. 26, No. 1, 549--596 (2016; Zbl 1408.53109) Full Text: DOI arXiv Euclid
Dasgupta, Ratan Optimal choice of small regular shapes for accidentally damaged tessellation. (English) Zbl 1338.60023 Dasgupta, Ratan (ed.), Growth curve and structural equation modeling. Topics from the Indian Statistical Institute. Based on the presentations at the growth curve models, GCM, workshop, Giridih, India, February 18–19, 2014. Cham: Springer (ISBN 978-3-319-17328-3/hbk; 978-3-319-17329-0/ebook). Springer Proceedings in Mathematics & Statistics 132, 287-299 (2015). MSC: 60D05 62P30 PDFBibTeX XMLCite \textit{R. Dasgupta}, Springer Proc. Math. Stat. 132, 287--299 (2015; Zbl 1338.60023) Full Text: DOI
Cantarella, Jason; Grosberg, Alexander Y.; Kusner, Robert; Shonkwiler, Clayton The expected total curvature of random polygons. (English) Zbl 1357.60017 Am. J. Math. 137, No. 2, 411-438 (2015). MSC: 60D05 53A04 PDFBibTeX XMLCite \textit{J. Cantarella} et al., Am. J. Math. 137, No. 2, 411--438 (2015; Zbl 1357.60017) Full Text: DOI arXiv Link
Fabila-Monroy, Ruy; Huemer, Clemens; Mitsche, Dieter Empty non-convex and convex four-gons in random point sets. (English) Zbl 1363.60004 Stud. Sci. Math. Hung. 52, No. 1, 52-64 (2015). Reviewer: Viktor Ohanyan (Erevan) MSC: 60D05 52A22 PDFBibTeX XMLCite \textit{R. Fabila-Monroy} et al., Stud. Sci. Math. Hung. 52, No. 1, 52--64 (2015; Zbl 1363.60004) Full Text: DOI
Fodor, F.; Kevei, P.; Vígh, V. On random disc polygons in smooth convex discs. (English) Zbl 1314.52004 Adv. Appl. Probab. 46, No. 4, 899-918 (2014). Reviewer: Florian Pausinger (Klosterneuburg) MSC: 52A22 60D05 PDFBibTeX XMLCite \textit{F. Fodor} et al., Adv. Appl. Probab. 46, No. 4, 899--918 (2014; Zbl 1314.52004) Full Text: DOI Euclid
Ballani, Felix; van den Boogaart, Karl Gerald Weighted Poisson cells as models for random convex polytopes. (English) Zbl 1319.60011 Methodol. Comput. Appl. Probab. 16, No. 2, 369-384 (2014). MSC: 60D05 62B05 60G55 PDFBibTeX XMLCite \textit{F. Ballani} and \textit{K. G. van den Boogaart}, Methodol. Comput. Appl. Probab. 16, No. 2, 369--384 (2014; Zbl 1319.60011) Full Text: DOI
Cantarella, Jason; Deguchi, Tetsuo; Shonkwiler, Clayton Probability theory of random polygons from the quaternionic viewpoint. (English) Zbl 1300.60026 Commun. Pure Appl. Math. 67, No. 10, 1658-1699 (2014). MSC: 60D05 52A22 PDFBibTeX XMLCite \textit{J. Cantarella} et al., Commun. Pure Appl. Math. 67, No. 10, 1658--1699 (2014; Zbl 1300.60026) Full Text: DOI arXiv
Beermann, Mareen; Redenbach, Claudia; Thäle, Christoph Asymptotic shape of small cells. (English) Zbl 1296.60018 Math. Nachr. 287, No. 7, 737-747 (2014). MSC: 60D05 60G55 52A22 PDFBibTeX XMLCite \textit{M. Beermann} et al., Math. Nachr. 287, No. 7, 737--747 (2014; Zbl 1296.60018) Full Text: DOI arXiv
Bäsel, U. Random chords and point distances in regular polygons. (English) Zbl 1324.60005 Acta Math. Univ. Comen., New Ser. 83, No. 1, 1-18 (2014). Reviewer: Jan Rataj (Prague) MSC: 60D05 PDFBibTeX XMLCite \textit{U. Bäsel}, Acta Math. Univ. Comen., New Ser. 83, No. 1, 1--18 (2014; Zbl 1324.60005) Full Text: arXiv
Koroleva, E. V.; Nikitin, Ya. Yu. \(U\)-max-statistics and limit theorems for perimeters and areas of random polygons. (English) Zbl 1293.60032 J. Multivariate Anal. 127, 98-111 (2014). Reviewer: Neville Weber (Sydney) MSC: 60F05 62G32 62H11 PDFBibTeX XMLCite \textit{E. V. Koroleva} and \textit{Ya. Yu. Nikitin}, J. Multivariate Anal. 127, 98--111 (2014; Zbl 1293.60032) Full Text: DOI arXiv
El Machkouri, Mohamed On the asymptotic normality of frequency polygons for strongly mixing spatial processes. (English) Zbl 1292.62054 Stat. Inference Stoch. Process. 16, No. 3, 193-206 (2013). MSC: 62G05 62G20 62G07 60G60 PDFBibTeX XMLCite \textit{M. El Machkouri}, Stat. Inference Stoch. Process. 16, No. 3, 193--206 (2013; Zbl 1292.62054) Full Text: DOI arXiv HAL
Groeneboom, Piet Convex hulls of uniform samples from a convex polygon. (English) Zbl 1251.60011 Adv. Appl. Probab. 44, No. 2, 330-342 (2012). Reviewer: Viktor Ohanyan (Erevan) MSC: 60D05 52A22 60F05 60G55 PDFBibTeX XMLCite \textit{P. Groeneboom}, Adv. Appl. Probab. 44, No. 2, 330--342 (2012; Zbl 1251.60011) Full Text: DOI arXiv Euclid
Lejeune, F.-X. Piecewise linear density estimation for sampled data. (English) Zbl 1323.62030 Math. Methods Stat. 20, No. 2, 106-124 (2011). MSC: 62G07 62M09 60G10 PDFBibTeX XMLCite \textit{F. X. Lejeune}, Math. Methods Stat. 20, No. 2, 106--124 (2011; Zbl 1323.62030) Full Text: DOI arXiv
Yershov, A. V. Limit theorems for random polygons. (Ukrainian. English summary) Zbl 1249.60135 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2011, No. 3, 24-28 (2011). MSC: 60H10 60F99 PDFBibTeX XMLCite \textit{A. V. Yershov}, Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2011, No. 3, 24--28 (2011; Zbl 1249.60135)
Neddermeyer, Jan C. Computationally efficient nonparametric importance sampling. (English) Zbl 1388.62015 J. Am. Stat. Assoc. 104, No. 486, 788-802 (2009). MSC: 62D05 60J22 62G07 PDFBibTeX XMLCite \textit{J. C. Neddermeyer}, J. Am. Stat. Assoc. 104, No. 486, 788--802 (2009; Zbl 1388.62015) Full Text: DOI arXiv
Nienhuis, Bernard; Kager, Wouter Stochastic Löwner evolution and the scaling limit of critical models. (English) Zbl 1180.82033 Guttmann, Anthony J. (ed.), Polygons, polyominoes and polycubes. Dordrecht: Springer (ISBN 978-1-4020-9926-7/hbk; 978-1-4020-9927-4/ebook). Lecture Notes in Physics 775, 425-467 (2009). MSC: 82B20 82B27 82B41 60G50 60J65 82B43 PDFBibTeX XMLCite \textit{B. Nienhuis} and \textit{W. Kager}, Lect. Notes Phys. 775, 425--467 (2009; Zbl 1180.82033) Full Text: DOI arXiv
Ambartzumian, R. V. Integration of combinatorial decompositions in the presence of collinearities. (English. Russian original) Zbl 1153.60006 J. Contemp. Math. Anal., Armen. Acad. Sci. 43, No. 1, 3-20 (2008); translation from Izv. Nats. Akad. Nauk Armen., Mat. 43, No. 1, 5-29 (2008). Reviewer: Paolo Dulio (Milano) MSC: 60D05 52A22 PDFBibTeX XMLCite \textit{R. V. Ambartzumian}, J. Contemp. Math. Anal., Armen. Acad. Sci. 43, No. 1, 3--20 (2008; Zbl 1153.60006); translation from Izv. Nats. Akad. Nauk Armen., Mat. 43, No. 1, 5--29 (2008) Full Text: DOI
James, E. W.; Soteros, C. E. New pattern theorems for square lattice self-avoiding walks and self-avoiding polygons. (English) Zbl 1189.82047 J. Phys. A, Math. Theor. 40, No. 30, 8621-8634 (2007). Reviewer: Daniel Boivin (Brest) MSC: 82B41 60G50 PDFBibTeX XMLCite \textit{E. W. James} and \textit{C. E. Soteros}, J. Phys. A, Math. Theor. 40, No. 30, 8621--8634 (2007; Zbl 1189.82047) Full Text: DOI
Lawler, Gregory F.; Lind, Joan R. Two-sided \(\mathrm{SLE}_{8/3}\) and the infinite self-avoiding polygon. (English) Zbl 1133.60036 Binder, Ilia (ed.) et al., Universality and renormalization. From stochastic evolution to renormalization of quantum fields. Proceedings of the workshops ‘Percolation, SLE and related topics’, September 20–24 2005 and ‘Renormalization and universality in mathematical physics’, October 18–22, 2005, Toronto, Canada. Providence, RI: American Mathematical Society (AMS); Toronto: The Fields Institute for Research in Mathematical Sciences (ISBN 0-8218-4273-0/hbk). Fields Institute Communications 50, 249-280 (2007). Reviewer: Alexander V. Bulinskij (Moskva) MSC: 60K35 60G50 60J65 82B41 PDFBibTeX XMLCite \textit{G. F. Lawler} and \textit{J. R. Lind}, Fields Inst. Commun. 50, 249--280 (2007; Zbl 1133.60036)
Seneta, Eugene; Jongmans, François The problem of the broken rod and Ernesto Cesàro’s early work in probability. (English) Zbl 1084.60004 Math. Sci. 30, No. 2, 67-76 (2005). MSC: 60-03 01A55 60C05 60D05 PDFBibTeX XMLCite \textit{E. Seneta} and \textit{F. Jongmans}, Math. Sci. 30, No. 2, 67--76 (2005; Zbl 1084.60004)
Madras, Neal; Wu, C. Chris Self-avoiding walks on hyperbolic graphs. (English) Zbl 1139.82026 Comb. Probab. Comput. 14, No. 4, 523-548 (2005). Reviewer: Chengxun Wu (Shanghai) MSC: 82C20 82C27 60G50 05B45 52C20 60C05 PDFBibTeX XMLCite \textit{N. Madras} and \textit{C. C. Wu}, Comb. Probab. Comput. 14, No. 4, 523--548 (2005; Zbl 1139.82026) Full Text: DOI
Finch, Steven; Hueter, Irene Random convex hulls: a variance revisited. (English) Zbl 1068.60020 Adv. Appl. Probab. 36, No. 4, 981-986 (2004). Reviewer: Ilya S. Molchanov (Bern) MSC: 60D05 52A22 PDFBibTeX XMLCite \textit{S. Finch} and \textit{I. Hueter}, Adv. Appl. Probab. 36, No. 4, 981--986 (2004; Zbl 1068.60020) Full Text: DOI
Kenyon, Richard W.; Sheffield, Scott Dimers, tilings and trees. (English) Zbl 1055.05032 J. Comb. Theory, Ser. B 92, No. 2, 295-317 (2004). MSC: 05C05 05C70 05B45 60C05 60J10 60J20 PDFBibTeX XMLCite \textit{R. W. Kenyon} and \textit{S. Sheffield}, J. Comb. Theory, Ser. B 92, No. 2, 295--317 (2004; Zbl 1055.05032) Full Text: DOI arXiv
Miles, Roger E.; Mackisack, Margaret S. A large class of random tessellations with the classic Poisson polygon distributions. (English) Zbl 1474.60021 Forma 17, No. 1, 1-17 (2002). MSC: 60D05 PDFBibTeX XMLCite \textit{R. E. Miles} and \textit{M. S. Mackisack}, Forma 17, No. 1, 1--17 (2002; Zbl 1474.60021)
Hayen, A.; Quine, M. P. Areas of components of a Voronoi polygon in a homogeneous Poisson process in the plane. (English) Zbl 1008.60025 Adv. Appl. Probab. 34, No. 2, 281-291 (2002). Reviewer: V.Schmidt (Ulm) MSC: 60D05 PDFBibTeX XMLCite \textit{A. Hayen} and \textit{M. P. Quine}, Adv. Appl. Probab. 34, No. 2, 281--291 (2002; Zbl 1008.60025) Full Text: DOI
Bianchi, Gabriele Determining convex polygons from their covariograms. (English) Zbl 1030.52002 Adv. Appl. Probab. 34, No. 2, 261-266 (2002). Reviewer: W.Weil (Karlsruhe) MSC: 52A20 60D05 52A22 52A38 PDFBibTeX XMLCite \textit{G. Bianchi}, Adv. Appl. Probab. 34, No. 2, 261--266 (2002; Zbl 1030.52002) Full Text: DOI
Glaister, P. An invariance property of regular polygons for a problem in probability. (English) Zbl 1016.60011 Int. J. Math. Educ. Sci. Technol. 31, No. 2, 271-282 (2000). Reviewer: Paolo Dulio (Milano) MSC: 60D05 PDFBibTeX XMLCite \textit{P. Glaister}, Int. J. Math. Educ. Sci. Technol. 31, No. 2, 271--282 (2000; Zbl 1016.60011) Full Text: DOI
Feuerverger, Andrey; Hall, Peter Methods for density estimation in thick-slice versions of Wicksell’s problem. (English) Zbl 0995.62036 J. Am. Stat. Assoc. 95, No. 450, 535-546 (2000). MSC: 62G07 60D05 62P10 PDFBibTeX XMLCite \textit{A. Feuerverger} and \textit{P. Hall}, J. Am. Stat. Assoc. 95, No. 450, 535--546 (2000; Zbl 0995.62036) Full Text: DOI
Duma, Andrei; Stoka, Marius Geometric probabilities for non convex lattices. (English) Zbl 0967.60008 Ann. I.S.U.P. 44, No. 1, 35-46 (2000). Reviewer: I.C.Vladimirescu (Craiova) MSC: 60D05 52A22 PDFBibTeX XMLCite \textit{A. Duma} and \textit{M. Stoka}, Ann. I.S.U.P. 44, No. 1, 35--46 (2000; Zbl 0967.60008)
Molloy, Michael; Reed, Bruce; Steiger, William On the mixing rate of the triangulation walk. (English) Zbl 0918.60060 Pardalos, Panos (ed.) et al., Randomization methods in algorithm design. DIMACS workshop, Princeton Univ., NJ, USA, December 12–14, 1997. Providence, RI: AMS, American Mathematical Society. DIMACS, Ser. Discrete Math. Theor. Comput. Sci. 43, 179-190 (1999). MSC: 60G50 68R10 05C80 PDFBibTeX XMLCite \textit{M. Molloy} et al., DIMACS, Ser. Discrete Math. Theor. Comput. Sci. 43, 179--190 (1999; Zbl 0918.60060)
Rublev, B. V.; Petunin, Yu. I. Minimum-area ellipse containing a finite set of points. II. (English. Russian original) Zbl 0938.52002 Ukr. Math. J. 50, No. 8, 1253-1261 (1998); translation from Ukr. Mat. Zh. 50, No. 8, 1098-1105 (1998). Reviewer: O.A.Voina (Kyïv) MSC: 52A10 14H52 60J65 PDFBibTeX XMLCite \textit{B. V. Rublev} and \textit{Yu. I. Petunin}, Ukr. Mat. Zh. 50, No. 8, 1098--1105 (1998; Zbl 0938.52002); translation from Ukr. Mat. Zh. 50, No. 8, 1098--1105 (1998) Full Text: DOI
Rublev, B. V.; Petunin, Yu. I. Minimum-area ellipse containing a finite set of points. I. (English. Russian original) Zbl 0938.52001 Ukr. Math. J. 50, No. 7, 1115-1124 (1998); translation from Ukr. Mat. Zh. 50, No. 7, 980-988 (1998). Reviewer: O.A.Voina (Kyïv) MSC: 52A10 14H52 60J65 PDFBibTeX XMLCite \textit{B. V. Rublev} and \textit{Yu. I. Petunin}, Ukr. Mat. Zh. 50, No. 7, 980--989 (1998; Zbl 0938.52001); translation from Ukr. Mat. Zh. 50, No. 7, 980--988 (1998) Full Text: DOI
Hamadouche, D. Weak convergence of smoothed empirical process in Hölder spaces. (English) Zbl 0927.60032 Stat. Probab. Lett. 36, No. 4, 393-400 (1998). MSC: 60F05 60B10 62G30 PDFBibTeX XMLCite \textit{D. Hamadouche}, Stat. Probab. Lett. 36, No. 4, 393--400 (1998; Zbl 0927.60032) Full Text: DOI
Kovalenko, I. N. Proof of David Kendall’s conjecture concerning the shape of large random polygons. (English. Russian original) Zbl 0922.60022 Cybern. Syst. Anal. 33, No. 4, 461-467 (1997); translation from Kibern. Sist. Anal. 1997, No. 4, 3-10 (1997). Reviewer: V.Oganyan (Erevan) MSC: 60D05 52A22 PDFBibTeX XMLCite \textit{I. N. Kovalenko}, Cybern. Syst. Anal. 33, No. 4, 461--467 (1997; Zbl 0922.60022); translation from Kibern. Sist. Anal. 1997, No. 4, 3--10 (1997) Full Text: DOI
Shkarupa, E. V.; Voytishek, A. V. Optimization of discretely stochastic procedures for globally estimating the solution of an integral equation of the second kind. (English) Zbl 0891.65140 Russ. J. Numer. Anal. Math. Model. 12, No. 6, 525-546 (1997). Reviewer: N.Curteanu (Iaşi) MSC: 65R20 45F05 60H30 PDFBibTeX XMLCite \textit{E. V. Shkarupa} and \textit{A. V. Voytishek}, Russ. J. Numer. Anal. Math. Model. 12, No. 6, 525--546 (1997; Zbl 0891.65140) Full Text: DOI
Adler, Robert J.; Pyke, Ron Scanning Brownian processes. (English) Zbl 0895.60042 Adv. Appl. Probab. 29, No. 2, 295-326 (1997). Reviewer: T.Inglot (Wrocław) MSC: 60G15 60G17 60F15 60G60 PDFBibTeX XMLCite \textit{R. J. Adler} and \textit{R. Pyke}, Adv. Appl. Probab. 29, No. 2, 295--326 (1997; Zbl 0895.60042) Full Text: DOI
Molchanov, Ilya Statistical problems for random sets. (English) Zbl 0887.62095 Goutsias, John (ed.) et al., Random sets. Theory and applications. Proceedings of the IMA workshop, Minneapolis, MN, USA, 1996. New York, NY: Springer. IMA Vol. Math. Appl. 97, 27-45 (1997). Reviewer: L.Heinrich (Augsburg) MSC: 62M30 60D05 60G55 PDFBibTeX XMLCite \textit{I. Molchanov}, IMA Vol. Math. Appl. 97, 27--45 (1997; Zbl 0887.62095)
Buchta, Christian; Reitzner, Matthias On a theorem of G. Herglotz about random polygons. (English) Zbl 0896.52013 Stoka, Marius I. (ed.), Second international conference in stochastic geometry, convex bodies and empirical measures, Agrigento, Italy, September 9–14, 1996. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 50, 89-102 (1997). Reviewer: W.Weil (Karlsruhe) MSC: 52A22 60D05 PDFBibTeX XMLCite \textit{C. Buchta} and \textit{M. Reitzner}, in: Second international conference in stochastic geometry, convex bodies and empirical measures, Agrigento, Italy, September 9--14, 1996. Palermo: Circolo Matematico di Palermo. 89--102 (1997; Zbl 0896.52013)
Molchanov, I. S.; Stoyan, D. Statistical models of random polyhedra. (English) Zbl 0851.60010 Commun. Stat., Stochastic Models 12, No. 2, 199-214 (1996). MSC: 60D05 PDFBibTeX XMLCite \textit{I. S. Molchanov} and \textit{D. Stoyan}, Commun. Stat., Stochastic Models 12, No. 2, 199--214 (1996; Zbl 0851.60010) Full Text: DOI Link
Baryshnikov, Yu. Counting the shape of a drum. (English) Zbl 0851.52005 Adv. Appl. Math. 17, No. 1, 101-116 (1996). Reviewer: I.S.Molchanov (Glasgow) MSC: 52A22 60D05 PDFBibTeX XMLCite \textit{Yu. Baryshnikov}, Adv. Appl. Math. 17, No. 1, 101--116 (1996; Zbl 0851.52005) Full Text: DOI
Satyanarayana, A.; Wood, R. K.; Camarinopoulos, L.; Pampoukis, G. Note on “A linear-time algorithm for computing \(K\)-terminal reliability in a series-parallel network”. (English) Zbl 0856.90051 SIAM J. Comput. 25, No. 2, 290 (1996). MSC: 90B18 90C60 60C05 05A10 PDFBibTeX XMLCite \textit{A. Satyanarayana} et al., SIAM J. Comput. 25, No. 2, 290 (1996; Zbl 0856.90051) Full Text: DOI
Valtr, P Probability that \(n\) random points are in convex position. (English) Zbl 0820.60007 Discrete Comput. Geom. 13, No. 3-4, 637-643 (1995). Reviewer: R.A.Vitale (Stoors) MSC: 60D05 PDFBibTeX XMLCite \textit{P Valtr}, Discrete Comput. Geom. 13, No. 3--4, 637--643 (1995; Zbl 0820.60007) Full Text: DOI EuDML
Bennett-Wood, D.; Brak, R.; Guttmann, A. J.; Owczarek, A. L.; Prellberg, T. Low-temperature \(2D\) polymer partition function scaling: Series analysis results. (English) Zbl 0820.60102 J. Phys. A, Math. Gen. 27, No. 2, L1-L8 (1994). MSC: 60K40 82D99 PDFBibTeX XMLCite \textit{D. Bennett-Wood} et al., J. Phys. A, Math. Gen. 27, No. 2, L\, 1-L\, 8 (1994; Zbl 0820.60102) Full Text: DOI
Buchta, Christian On the probability that two sets of points have disjoint convex hulls. (English) Zbl 0809.52007 Stoka, Marius (ed.), First international conference on stochastic geometry, convex bodies and empirical measures, Palermo, Italy, 25 April - 2 May 1993. Palermo: Circolo Matemático di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 35, 67-74 (1994). Reviewer: I.S.Molchanov (Amsterdam) MSC: 52A22 60D05 PDFBibTeX XMLCite \textit{C. Buchta}, in: First international conference on stochastic geometry, convex bodies and empirical measures, Palermo, Italy, 25 April - 2 May 1993. Palermo: Circolo Matemático di Palermo. 67--74 (1994; Zbl 0809.52007)
Godefroy, Gilles [Duychaerts, C.; Hauw, J. J.] Poisson distribution and stereology. (Distribution de Poisson et stéréologie. (D’après C. Duyckaerts, G. Godefroy, J. J. Hauw).) (French) Zbl 0829.92005 Choquet, G. (ed.) et al., Séminaire d’initiation à l’analyse. 32ème année: 1992/1993. Paris: Université Pierre et Marie Curie, Publ. Math. Univ. Pierre Marie Curie. 109, Expo. No. 10, 7 p. (1993). Reviewer: A.Papadopoulos (Strasbourg) MSC: 92C20 92C50 60D05 PDFBibTeX XMLCite \textit{G. Godefroy}, in: Séminaire d'initiation à l'analyse. 32ème année: 1992/1993. Paris: Université Pierre et Marie Curie. Expo. No. 10, 7 p. (1993; Zbl 0829.92005)
Janse van Rensburg, E. J.; Orlandini, E.; Sumners, D. W.; Tesi, M. C.; Whittington, S. G. The writhe of a self-avoiding polygon. (English) Zbl 0804.60101 J. Phys. A, Math. Gen. 26, No. 19, L981-L986 (1993). MSC: 60K40 82D60 PDFBibTeX XMLCite \textit{E. J. Janse van Rensburg} et al., J. Phys. A, Math. Gen. 26, No. 19, L\, 981-L\, 986 (1993; Zbl 0804.60101) Full Text: DOI
Helms, L. L. Brownian motion in a closed convex polygon with normal reflection. (English) Zbl 0765.60080 Ann. Acad. Sci. Fenn., Ser. A I, Math. 17, No. 2, 199-209 (1992). Reviewer: M.Nisio (Rokko / Kobe) MSC: 60J65 60J35 60J25 PDFBibTeX XMLCite \textit{L. L. Helms}, Ann. Acad. Sci. Fenn., Ser. A I, Math. 17, No. 2, 199--209 (1992; Zbl 0765.60080) Full Text: DOI
Janse van Rensburg, E. J.; Whittington, S. G.; Madras, N. The pivot algorithm and polygons: Results on the FCC lattice. (English) Zbl 0714.65109 J. Phys. A, Math. Gen. 23, No. 9, 1589-1612 (1990). Reviewer: N.Bouleau MSC: 65C99 60G50 82B40 82C40 PDFBibTeX XMLCite \textit{E. J. Janse van Rensburg} et al., J. Phys. A, Math. Gen. 23, No. 9, 1589--1612 (1990; Zbl 0714.65109) Full Text: DOI
Abrahamson, Karl On the modality of convex polygons. (English) Zbl 0712.52006 Discrete Comput. Geom. 5, No. 4, 409-419 (1990). MSC: 52A22 60D05 PDFBibTeX XMLCite \textit{K. Abrahamson}, Discrete Comput. Geom. 5, No. 4, 409--419 (1990; Zbl 0712.52006) Full Text: DOI EuDML
Sidorowicz, Józef Penumbra in the heat diffraction on a polygon. (Russian) Zbl 0706.60062 Demonstr. Math. 22, No. 4, 939-953 (1989). Reviewer: J.Sidorowicz MSC: 60H15 60D05 PDFBibTeX XMLCite \textit{J. Sidorowicz}, Demonstr. Math. 22, No. 4, 939--953 (1989; Zbl 0706.60062) Full Text: DOI
Pippenger, Nicholas Knots in random walks. (English) Zbl 0681.57001 Discrete Appl. Math. 25, No. 3, 273-278 (1989). MSC: 57M25 60G50 82D60 PDFBibTeX XMLCite \textit{N. Pippenger}, Discrete Appl. Math. 25, No. 3, 273--278 (1989; Zbl 0681.57001) Full Text: DOI
Mecke, J. A note on Cowan’s process of space division. (English) Zbl 0678.60017 Adv. Appl. Probab. 21, No. 1, 235-236 (1989). Reviewer: J.-Cl.Massé MSC: 60D05 60J10 52A22 60K25 PDFBibTeX XMLCite \textit{J. Mecke}, Adv. Appl. Probab. 21, No. 1, 235--236 (1989; Zbl 0678.60017) Full Text: DOI
Cowan, Richard The division of space and the Poisson distribution. (English) Zbl 0678.60016 Adv. Appl. Probab. 21, No. 1, 233-234 (1989). Reviewer: J-Cl.Massé MSC: 60D05 60J10 52A22 PDFBibTeX XMLCite \textit{R. Cowan}, Adv. Appl. Probab. 21, No. 1, 233--234 (1989; Zbl 0678.60016) Full Text: DOI
Nagajev, A. V.; Goldfield, S. M. The limit theorem for the uniform distribution on the circumference. (English) Zbl 0678.60015 Wiss. Z. Tech. Univ. Dres. 38, No. 1, 163-165 (1989). Reviewer: W.Weil MSC: 60D05 52A22 60F05 PDFBibTeX XMLCite \textit{A. V. Nagajev} and \textit{S. M. Goldfield}, Wiss. Z. Tech. Univ. Dres. 38, No. 1, 163--165 (1989; Zbl 0678.60015)
Ştefănescu, Ştefan On some problems in geometric probability. (English) Zbl 0739.60011 An. Univ. Bucur., Mat. 38, No. 3, 67-74 (1989). Reviewer: W.Weil (Karlsruhe) MSC: 60D05 PDFBibTeX XMLCite \textit{Ş. Ştefănescu}, An. Univ. Bucur., Mat. 38, No. 3, 67--74 (1989; Zbl 0739.60011)
Rejali, Ali Asymptotic normality of the area under a random increasing lattice polygon. (English) Zbl 0705.60015 Bull. Iran. Math. Soc. 15, No. 1, 49-56 (1988). MSC: 60D05 60F05 PDFBibTeX XMLCite \textit{A. Rejali}, Bull. Iran. Math. Soc. 15, No. 1, 49--56 (1988; Zbl 0705.60015)
Madras, Neal End patterns of self-avoiding walks. (English) Zbl 0678.60061 J. Stat. Phys. 53, No. 3-4, 689-701 (1988). MSC: 60G50 PDFBibTeX XMLCite \textit{N. Madras}, J. Stat. Phys. 53, No. 3--4, 689--701 (1988; Zbl 0678.60061) Full Text: DOI
Constantin, R. F. The convex hull of random n-points in a convex r-polygon of the space \(M_ 2\). (Romanian) Zbl 0655.52005 Geometry and topology, Proc. 17th Natl. Conf., Tîrgovişte/Rom. 1986, 43-48 (1988). Reviewer: M.Turinici MSC: 52A22 60D05 51B20 PDFBibTeX XML
Groeneboom, Piet Limit theorems for convex hulls. (English) Zbl 0635.60012 Probab. Theory Relat. Fields 79, No. 3, 327-368 (1988). Reviewer: P.Groeneboom MSC: 60D05 60F05 60G55 60G44 PDFBibTeX XMLCite \textit{P. Groeneboom}, Probab. Theory Relat. Fields 79, No. 3, 327--368 (1988; Zbl 0635.60012) Full Text: DOI
Mikkov, P. An estimate for the volume of a set of polygonal patterns. (English) Zbl 0737.60017 Uch. Zap. Tartu. Gos. Univ. 798, 57-67 (1988). Reviewer: I.S.Molchanov (Kiev) MSC: 60D05 60G60 60J99 PDFBibTeX XML
Kerner, R.; Santos, D. M. A model of growth of crystalline and amorphous structures. Application to Penrose tilings. (English) Zbl 0706.51020 Differential geometric methods in theoretical physics, Proc. 15th Int. Conf., DGM, Clausthal/FRG 1986, 415-422 (1987). Reviewer: I.S.Molchanov MSC: 51M20 60D05 82D25 51E30 52C22 PDFBibTeX XML
Kendall, David G.; Le, Hui-Lin The structure and explicit determination of convex-polygonally generated shape-densities. (English) Zbl 0634.60011 Adv. Appl. Probab. 19, 896-916 (1987). Reviewer: K.Schürger MSC: 60D05 52A22 52A37 PDFBibTeX XMLCite \textit{D. G. Kendall} and \textit{H.-L. Le}, Adv. Appl. Probab. 19, 896--916 (1987; Zbl 0634.60011) Full Text: DOI
Mecke, J. Extremal properties of some geometric processes. (English) Zbl 0633.60017 Acta Appl. Math. 9, 61-69 (1987). Reviewer: I.Molchanov MSC: 60D05 60G55 PDFBibTeX XMLCite \textit{J. Mecke}, Acta Appl. Math. 9, 61--69 (1987; Zbl 0633.60017) Full Text: DOI
Waksman, Peter Plane polygons and a conjecture of Blaschke. (English) Zbl 0581.52005 Adv. Appl. Probab. 17, 774-793 (1985). Reviewer: W.Weil MSC: 52A22 52A10 60D05 PDFBibTeX XMLCite \textit{P. Waksman}, Adv. Appl. Probab. 17, 774--793 (1985; Zbl 0581.52005) Full Text: DOI
Buchta, Christian Stochastische Approximation konvexer Polygone. (German) Zbl 0536.60020 Z. Wahrscheinlichkeitstheor. Verw. Geb. 67, 283-304 (1984). MSC: 60D05 52A22 60F99 PDFBibTeX XMLCite \textit{C. Buchta}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 67, 283--304 (1984; Zbl 0536.60020) Full Text: DOI
Kuchkarov, Ya. A functional law of iterated logarithm for random polygons generated by symmetrically dependent random variables. (Russian) Zbl 0629.60043 Dokl. Akad. Nauk UzSSR 1983, No. 8, 3-4 (1983). Reviewer: Z.G.Gorgadze MSC: 60F17 PDFBibTeX XMLCite \textit{Ya. Kuchkarov}, Dokl. Akad. Nauk UzSSR 1983, No. 8, 3--4 (1983; Zbl 0629.60043)
Tanner, J. C. Polygons formed by random lines in a plane: Some further results. (English) Zbl 0532.60014 J. Appl. Probab. 20, 778-787 (1983). Reviewer: W.Weil MSC: 60D05 60G55 PDFBibTeX XMLCite \textit{J. C. Tanner}, J. Appl. Probab. 20, 778--787 (1983; Zbl 0532.60014) Full Text: DOI
Haigh, Gordon; Jones, David Pierce A random polygon and \(n\)-dimensional volume. (English) Zbl 0521.60010 Math. Gaz. 67, 89-92 (1983). MSC: 60D05 52A22 PDFBibTeX XMLCite \textit{G. Haigh} and \textit{D. P. Jones}, Math. Gaz. 67, 89--92 (1983; Zbl 0521.60010) Full Text: DOI
Gates, J. Recognition of triangles and quadrilaterals by chord length distribution. (English) Zbl 0504.60015 J. Appl. Probab. 19, 873-879 (1982). MSC: 60D05 52A22 PDFBibTeX XMLCite \textit{J. Gates}, J. Appl. Probab. 19, 873--879 (1982; Zbl 0504.60015) Full Text: DOI
DiDonato, A. R.; Hageman, R. K. A method for computing the integral of the bivariate normal distribution over an arbitrary polygon. (English) Zbl 0489.65078 SIAM J. Sci. Stat. Comput. 3, 434-446 (1982). MSC: 65C99 60E99 62E99 PDFBibTeX XMLCite \textit{A. R. DiDonato} and \textit{R. K. Hageman}, SIAM J. Sci. Stat. Comput. 3, 434--446 (1982; Zbl 0489.65078) Full Text: DOI
Miles, R. E.; Maillardet, R. J. The basic structures of Voronoi and generalized Voronoi polygons. (English) Zbl 0482.60015 Essays in statistical science, Pap. in Honour of P.A.P. Moran, J. Appl. Probab., Spec. Vol. 19A, 97-111 (1982). MSC: 60D05 PDFBibTeX XML
Mecke, J. Palm methods for stationary random mosaics. (English) Zbl 0471.60019 Combinatorial principles in stochastic geometry, Work Collect., Erevan 1980, 124-132 (1980). MSC: 60D05 60G55 PDFBibTeX XML
Miller, W. J. C.; Biddle, D. Solution of question 8837. (Solution of question 8837.) (English) JFM 19.0206.01 Ed. Times XLVII. 41-44 (1887). Reviewer: Lampe, Prof. (Berlin) MSC: 60D05 PDFBibTeX XML