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Persistent Betti numbers are a major tool in persistent homology, a subfield of topological data analysis.
Uniqueness of the infinite cluster and related results in percolation
Aizenman, M., Kesten, H. and Newman, C · 1987
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Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation
Aizenman, M., Kesten, H. and Newman, C. M · 1987
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Growth rates of Euclidean minimal spanning trees with power weighted edges
Steele, J. M · 1988
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Density and uniqueness in percolation
Burton, R. M. and Keane, M · 1989
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Multivariate spatial central limit theorems with applications to percolation and spatial graphs
Penrose, M. D · 1991
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The central limit theorem for weighted minimal spanning trees on random points
Kesten, H. and Lee, S · 1996
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Continuum percolation
Meester, R. and Roy, R · 1996
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Co-existence of the occupied and vacant phase in boolean models in three or more dimensions
Sarkar, A · 1997
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Asymptotics for Voronoi tessellations on random samples
McGivney, K. and Yukich, J · 1999
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Topological persistence and simplification
Edelsbrunner, H., Letscher, D. and Zomorodian, A · 2000
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Asymptotics for weighted minimal spanning trees on random points
Yukich, J · 2000
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Central limit theorems for some graphs in computational geometry
Penrose, M. D. and Yukich, J. E · 2001
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Random geometric graphs
Penrose, M · 2003
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Weak laws of large numbers in geometric probability
Penrose, M. D. and Yukich, J. E · 2003
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Gaussian limits for random measures in geometric probability
Baryshnikov, Y. and Yukich, J. E · 2005
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Zomorodian, A. and Carlsson, G · 2005
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Gaussian limts for random geometric measures
Penrose, M · 2007
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Topology and data
Carlsson, G · 2009
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Topological methods for exploring low-density states in biomolecular folding pathways
Yao, Y., Sun, J., Huang, X., Bowman, G. R., Singh, G., Lesnick, M., Guibas, L. J., Pande, V. S. and Carlsson, G · 2009
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Random geometric complexes
Kahle, M · 2011
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Limit theorems for Betti numbers of random simplicial complexes
Kahle, M. and Meckes, E · 2013
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Topology of random geometric complexes: a survey
Bobrowski, O. and Kahle, M · 2018
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The density of expected persistence diagrams and its kernel based estimation
Chazal, F. and Divol, V · 2018
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Topological data analysis of financial time series: Landscapes of crashes
Gidea, M. and Katz, Y · 2018
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Limit theorems for persistence diagrams
Hiraoka, Y., Shirai, T. and Trinh, K. D · 2018
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Limit theorems for Betti numbers of extreme sample clouds with application to persistence barcodes
Owada, T · 2018
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Topological data analysis
Wasserman, L · 2018
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Probability theory: a comprehensive course
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Persistence theory: from quiver representations to data analysis
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On the topology of random complexes built over stationary point processes
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Topological data analysis of critical transitions in financial networks
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