Hirsch, Christian; Owada, Takashi Large deviation principle for geometric and topological functionals and associated point processes. (English) Zbl 07787930 Ann. Appl. Probab. 33, No. 5, 4008-4043 (2023). MSC: 60F10 60D05 60G55 55U10 58E05 PDFBibTeX XMLCite \textit{C. Hirsch} and \textit{T. Owada}, Ann. Appl. Probab. 33, No. 5, 4008--4043 (2023; Zbl 07787930) Full Text: DOI arXiv Link
Bonnet, Gilles; Hirsch, Christian; Rosen, Daniel; Willhalm, Daniel Limit theory of sparse random geometric graphs in high dimensions. (English) Zbl 1519.05215 Stochastic Processes Appl. 163, 203-236 (2023). MSC: 05C80 05C42 60D05 55U10 60F17 PDFBibTeX XMLCite \textit{G. Bonnet} et al., Stochastic Processes Appl. 163, 203--236 (2023; Zbl 1519.05215) Full Text: DOI arXiv
Gluzberg, Victor E.; Katz, Yuri A. Topological data analysis of noise: uniform unimodal distributions. (English) Zbl 1524.62628 Commun. Nonlinear Sci. Numer. Simul. 121, Article ID 107216, 26 p. (2023). MSC: 62R40 55N31 60G55 PDFBibTeX XMLCite \textit{V. E. Gluzberg} and \textit{Y. A. Katz}, Commun. Nonlinear Sci. Numer. Simul. 121, Article ID 107216, 26 p. (2023; Zbl 1524.62628) Full Text: DOI
Owada, Takashi Limit theory for \(U\)-statistics under geometric and topological constraints with rare events. (English) Zbl 1509.60016 J. Appl. Probab. 60, No. 1, 314-340 (2023). MSC: 60D05 60G55 55U10 60G70 PDFBibTeX XMLCite \textit{T. Owada}, J. Appl. Probab. 60, No. 1, 314--340 (2023; Zbl 1509.60016) Full Text: DOI
de Kergorlay, Henry-Louis; Tillmann, Ulrike; Vipond, Oliver Random Čech complexes on manifolds with boundary. (English) Zbl 07751079 Random Struct. Algorithms 61, No. 2, 309-352 (2022). Reviewer: Nikolaos Fountoulakis (Birmingham) MSC: 55N31 05E45 60D05 PDFBibTeX XMLCite \textit{H.-L. de Kergorlay} et al., Random Struct. Algorithms 61, No. 2, 309--352 (2022; Zbl 07751079) Full Text: DOI arXiv OA License
Owada, Takashi Convergence of persistence diagram in the sparse regime. (English) Zbl 1507.55009 Ann. Appl. Probab. 32, No. 6, 4706-4736 (2022). MSC: 55N31 55U10 60F05 60F15 60G55 PDFBibTeX XMLCite \textit{T. Owada}, Ann. Appl. Probab. 32, No. 6, 4706--4736 (2022; Zbl 1507.55009) Full Text: DOI arXiv
Bobrowski, Omer; Krioukov, Dmitri Random simplicial complexes: models and phenomena. (English) Zbl 1504.60004 Battiston, Federico (ed.) et al., Higher-order systems. Cham: Springer. Underst. Complex Syst., 59-96 (2022). MSC: 60-02 55-02 55U10 05E45 60D05 05C80 PDFBibTeX XMLCite \textit{O. Bobrowski} and \textit{D. Krioukov}, in: Higher-order systems. Cham: Springer. 59--96 (2022; Zbl 1504.60004) Full Text: DOI arXiv
Owada, Takashi; Wei, Zifu Functional strong law of large numbers for Betti numbers in the tail. (English) Zbl 1508.60042 Extremes 25, No. 4, 655-693 (2022). MSC: 60F15 60G70 55U10 60D05 60F17 PDFBibTeX XMLCite \textit{T. Owada} and \textit{Z. Wei}, Extremes 25, No. 4, 655--693 (2022; Zbl 1508.60042) Full Text: DOI arXiv
Bobrowski, Omer Homological connectivity in random Čech complexes. (English) Zbl 1493.05299 Probab. Theory Relat. Fields 183, No. 3-4, 715-788 (2022). MSC: 05E45 60D05 55U10 05C80 PDFBibTeX XMLCite \textit{O. Bobrowski}, Probab. Theory Relat. Fields 183, No. 3--4, 715--788 (2022; Zbl 1493.05299) Full Text: DOI arXiv
Thomas, Andrew M.; Owada, Takashi Functional limit theorems for the Euler characteristic process in the critical regime. (English) Zbl 1493.60065 Adv. Appl. Probab. 53, No. 1, 57-80 (2021). MSC: 60F17 55U10 60C05 60D05 PDFBibTeX XMLCite \textit{A. M. Thomas} and \textit{T. Owada}, Adv. Appl. Probab. 53, No. 1, 57--80 (2021; Zbl 1493.60065) Full Text: DOI arXiv
Thomas, Andrew M.; Owada, Takashi Functional strong laws of large numbers for Euler characteristic processes of extreme sample clouds. (English) Zbl 1479.60065 Extremes 24, No. 4, 699-724 (2021). MSC: 60F15 60G70 55U10 60F17 PDFBibTeX XMLCite \textit{A. M. Thomas} and \textit{T. Owada}, Extremes 24, No. 4, 699--724 (2021; Zbl 1479.60065) Full Text: DOI arXiv
Owada, Takashi; Samorodnitsky, Gennady; Thoppe, Gugan Limit theorems for topological invariants of the dynamic multi-parameter simplicial complex. (English) Zbl 1469.60100 Stochastic Processes Appl. 138, 56-95 (2021). MSC: 60F17 55U05 60C05 60F15 PDFBibTeX XMLCite \textit{T. Owada} et al., Stochastic Processes Appl. 138, 56--95 (2021; Zbl 1469.60100) Full Text: DOI arXiv Link
Akinwande, Grace; Reitzner, Matthias Multivariate central limit theorems for random simplicial complexes. (English) Zbl 1459.60017 Adv. Appl. Math. 121, Article ID 102076, 27 p. (2020). MSC: 60D05 60F05 55U10 PDFBibTeX XMLCite \textit{G. Akinwande} and \textit{M. Reitzner}, Adv. Appl. Math. 121, Article ID 102076, 27 p. (2020; Zbl 1459.60017) Full Text: DOI arXiv
Belton, Robin Lynne; Fasy, Brittany Terese; Mertz, Rostik; Micka, Samuel; Millman, David L.; Salinas, Daniel; Schenfisch, Anna; Schupbach, Jordan; Williams, Lucia Reconstructing embedded graphs from persistence diagrams. (English) Zbl 1476.68271 Comput. Geom. 90, Article ID 101658, 17 p. (2020). MSC: 68U05 55N31 68R10 68U03 PDFBibTeX XMLCite \textit{R. L. Belton} et al., Comput. Geom. 90, Article ID 101658, 17 p. (2020; Zbl 1476.68271) Full Text: DOI arXiv
Edelsbrunner, Herbert; Nikitenko, Anton; Ölsböck, Katharina; Synak, Peter Radius functions on Poisson-Delaunay mosaics and related complexes experimentally. (English) Zbl 1448.62215 Baas, Nils (ed.) et al., Topological data analysis. Proceedings of the Abel symposium 2018, Geiranger, Norway, June 4–8, 2018. Cham: Springer. Abel Symp. 15, 181-218 (2020). MSC: 62R40 60D05 55N31 PDFBibTeX XMLCite \textit{H. Edelsbrunner} et al., Abel Symp. 15, 181--218 (2020; Zbl 1448.62215) Full Text: DOI
Adams, Henry; Aminian, Manuchehr; Farnell, Elin; Kirby, Michael; Mirth, Joshua; Neville, Rachel; Peterson, Chris; Shonkwiler, Clayton A fractal dimension for measures via persistent homology. (English) Zbl 1448.62211 Baas, Nils (ed.) et al., Topological data analysis. Proceedings of the Abel symposium 2018, Geiranger, Norway, June 4–8, 2018. Cham: Springer. Abel Symp. 15, 1-31 (2020). MSC: 62R40 62R20 55N31 60B05 37F35 60F15 PDFBibTeX XMLCite \textit{H. Adams} et al., Abel Symp. 15, 1--31 (2020; Zbl 1448.62211) Full Text: DOI arXiv
Owada, Takashi; Thomas, Andrew M. Limit theorems for process-level Betti numbers for sparse and critical regimes. (English) Zbl 1456.60044 Adv. Appl. Probab. 52, No. 1, 1-31 (2020). Reviewer: Andrew Wade (Durham) MSC: 60D05 55U10 60F05 05E45 PDFBibTeX XMLCite \textit{T. Owada} and \textit{A. M. Thomas}, Adv. Appl. Probab. 52, No. 1, 1--31 (2020; Zbl 1456.60044) Full Text: DOI arXiv
Biscio, Christophe A. N.; Chenavier, Nicolas; Hirsch, Christian; Svane, Anne Marie Testing goodness of fit for point processes via topological data analysis. (English) Zbl 1440.62409 Electron. J. Stat. 14, No. 1, 1024-1074 (2020). MSC: 62R40 62G10 62H20 60D05 60G55 60F17 55N20 PDFBibTeX XMLCite \textit{C. A. N. Biscio} et al., Electron. J. Stat. 14, No. 1, 1024--1074 (2020; Zbl 1440.62409) Full Text: DOI arXiv Euclid
Feragen, Aasa (ed.); Hotz, Thomas (ed.); Huckemann, Stephan (ed.); Miller, Ezra (ed.) Statistics for data with geometric structure. Abstracts from the workshop held January 21–27, 2018. (English) Zbl 1409.00087 Oberwolfach Rep. 15, No. 1, 125-186 (2018). MSC: 00B05 00B25 62-06 62-07 62Hxx 53-06 55N35 65Cxx 60D05 14T05 PDFBibTeX XMLCite \textit{A. Feragen} (ed.) et al., Oberwolfach Rep. 15, No. 1, 125--186 (2018; Zbl 1409.00087) Full Text: DOI
Chazal, Frédéric; Fasy, Brittany; Lecci, Fabrizio; Michel, Bertrand; Rinaldo, Alessandro; Wasserman, Larry Robust topological inference: distance to a measure and kernel distance. (English) Zbl 1435.62452 J. Mach. Learn. Res. 18(2017-2018), Paper No. 159, 40 p. (2018). MSC: 62R40 55N31 62G32 62G35 PDFBibTeX XMLCite \textit{F. Chazal} et al., J. Mach. Learn. Res. 18, Paper No. 159, 40 p. (2018; Zbl 1435.62452) Full Text: arXiv Link
Hiraoka, Yasuaki; Shirai, Tomoyuki; Trinh, Khanh Duy Limit theorems for persistence diagrams. (English) Zbl 1402.60059 Ann. Appl. Probab. 28, No. 5, 2740-2780 (2018). MSC: 60G55 60B10 55N20 60G10 PDFBibTeX XMLCite \textit{Y. Hiraoka} et al., Ann. Appl. Probab. 28, No. 5, 2740--2780 (2018; Zbl 1402.60059) Full Text: DOI arXiv Euclid
Bobrowski, Omer; Kahle, Matthew Topology of random geometric complexes: a survey. (English) Zbl 1402.60015 J. Appl. Comput. Topol. 1, No. 3-4, 331-364 (2018). MSC: 60D05 60B99 55U10 60-02 PDFBibTeX XMLCite \textit{O. Bobrowski} and \textit{M. Kahle}, J. Appl. Comput. Topol. 1, No. 3--4, 331--364 (2018; Zbl 1402.60015) Full Text: DOI arXiv
Yogeshwaran, D.; Subag, Eliran; Adler, Robert J. Random geometric complexes in the thermodynamic regime. (English) Zbl 1366.60033 Probab. Theory Relat. Fields 167, No. 1-2, 107-142 (2017). Reviewer: Viktor Ohanyan (Erevan) MSC: 60D05 60G55 60F05 55U10 PDFBibTeX XMLCite \textit{D. Yogeshwaran} et al., Probab. Theory Relat. Fields 167, No. 1--2, 107--142 (2017; Zbl 1366.60033) Full Text: DOI arXiv
Yogeshwaran, D.; Adler, Robert J. On the topology of random complexes built over stationary point processes. (English) Zbl 1328.60123 Ann. Appl. Probab. 25, No. 6, 3338-3380 (2015). MSC: 60G55 60D05 60G10 05E45 55U10 05C10 58K05 PDFBibTeX XMLCite \textit{D. Yogeshwaran} and \textit{R. J. Adler}, Ann. Appl. Probab. 25, No. 6, 3338--3380 (2015; Zbl 1328.60123) Full Text: DOI arXiv Euclid
Bobrowski, Omer; Mukherjee, Sayan The topology of probability distributions on manifolds. (English) Zbl 1316.60020 Probab. Theory Relat. Fields 161, No. 3-4, 651-686 (2015). MSC: 60D05 60F15 60G55 55U10 PDFBibTeX XMLCite \textit{O. Bobrowski} and \textit{S. Mukherjee}, Probab. Theory Relat. Fields 161, No. 3--4, 651--686 (2015; Zbl 1316.60020) Full Text: DOI arXiv
Fasy, Brittany Terese; Lecci, Fabrizio; Rinaldo, Alessandro; Wasserman, Larry; Balakrishnan, Sivaraman; Singh, Aarti Confidence sets for persistence diagrams. (English) Zbl 1310.62059 Ann. Stat. 42, No. 6, 2301-2339 (2014). MSC: 62G15 62G07 62G20 62H12 55N35 PDFBibTeX XMLCite \textit{B. T. Fasy} et al., Ann. Stat. 42, No. 6, 2301--2339 (2014; Zbl 1310.62059) Full Text: DOI arXiv Euclid