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We initiate the study of persistent homology of random geometric simplicial complexes.
On the imbedding of systems of compacta in simplicial complexes
Karol Borsuk · 1948
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On random graphs. I
Paul Erdős and Alfréd Rényi · 1959
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Normal and integral currents
Herbert Federer and Wendell H. Fleming · 1960
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On the evolution of random graphs
Paul Erdős and Alfréd Rényi · 1961
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Elements of algebraic topology
James R. Munkres · 1984
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The union of balls and its dual shape
Herbert Edelsbrunner · 1993
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The union of balls and its dual shape
H. Edelsbrunner · 1995
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The longest edge of the random minimal spanning tree
Mathew D. Penrose · 1997
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The connectivity of a graph on uniform points on [ 0 , 1 ] d [0,1]^{d}
Martin JB Appel and Ralph P. Russo · 2002
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Algebraic topology
Allen Hatcher · 2002
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Mathematical results on scale-free random graphs
Béla Bollobás and Oliver M Riordan · 2003
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Random geometric graphs
Mathew Penrose · 2003
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Computing persistent homology
Afra Zomorodian and Gunnar Carlsson · 2005
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Nearest-neighbor searching and metric space dimensions
Kenneth L Clarkson · 2006
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Notes on Gromov’s systolic estimate
Larry Guth · 2006
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Homological connectivity of random 2-complexes
Nathan Linial and Roy Meshulam · 2006
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A statistical approach to persistent homology
Peter Bubenik and Peter T. Kim · 2007
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Coverage in sensor networks via persistent homology
Vin de Silva and Robert Ghrist · 2007
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On the local behavior of spaces of natural images
Gunnar Carlsson, Tigran Ishkhanov, Vin De Silva, and Afra Zomorodian · 2008
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Barcodes: the persistent topology of data
Robert Ghrist · 2008
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Topology and data
Gunnar Carlsson · 2009
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Mesh enhanced persistent homology
Benoit Hudson, Gary L. Miller, Steve Y. Oudot, and Donald R. Sheehy · 2009
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Topology of random clique complexes
Matthew Kahle · 2009
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Scalar field analysis over point cloud data
Frédéric Chazal, Leonidas J Guibas, Steve Y Oudot, and Primoz Skraba · 2011
Cited alongside, same era.
Random geometric complexes
Matthew Kahle · 2011
The topology of probability distributions on manifolds
Omer Bobrowski and Sayan Mukherjee · 2014
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Topological consistency via kernel estimation
Omer Bobrowski, Sayan Mukherjee, and Jonathan Taylor · 2014
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Persistence stability for geometric complexes
Frédéric Chazal, Vin De Silva, and Steve Oudot · 2014
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Stochastic convergence of persistence landscapes and silhouettes
Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, and Larry A. Wasserman · 2014
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Convergence rates for persistence diagram estimation in topological data analysis
Frédéric Chazal, Marc Glisse, Catherine Labruère, and Bertrand Michel · 2014
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Confidence sets for persistence diagrams
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Cited alongside, same era.
Euler integration of Gaussian random fields and persistent homology
Omer Bobrowski and Matthew Strom Borman · 2012
Cited alongside, same era.
Large convex holes in random point sets
József Balogh, Hernán González-Aguilar, and Gelasio Salazar · 2013
Cited alongside, same era.
On the bootstrap for persistence diagrams and landscapes
Frédéric Chazal, Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Aarti Singh, and Larry Wasserman · 2013
Cited alongside, same era.
Persistence-based clustering in riemannian manifolds
Frédéric Chazal, Leonidas J Guibas, Steve Y Oudot, and Primoz Skraba · 2013
Cited alongside, same era.
Limit theorems for Betti numbers of random simplicial complexes
Matthew Kahle and Elizabeth Meckes · 2013
Cited alongside, same era.
Brittany Terese Fasy, Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman, Sivaraman Balakrishnan, and Aarti Singh · 2014
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Sharp vanishing thresholds for cohomology of random flag complexes
Matthew Kahle · 2014
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The persistent homology of distance functions under random projection
Donald R. Sheehy · 2014
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Random geometric complexes in the thermodynamic regime
D. Yogeshwaran, Eliran Subag, and Robert J. Adler · 2014
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When does the top homology of a random simplicial complex vanish?
Lior Aronshtam and Nathan Linial · 2015
Closest in time.
PHAT (Persistent Homology Algorithm Toolbox), 2014
Ulrich Bauer, Michael Kerber, and Jan Reininghaus · 2015
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On the vanishing of homology in random Čech complexes
Omer Bobrowski and Shmuel Weinberger · 2015
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Efficient and robust persistent homology for measures
Mickaël Buchet, Frédéric Chazal, Steve Oudot, and Donald R. Sheehy · 2015
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Graph induced complex on point data
Tamal K Dey, Fengtao Fan, and Yusu Wang · 2015
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Limit theorems for point processes under geometric constraints (and topological crackle)
Takashi Owada and Robert J Adler · 2015
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CGAL User and Reference Manual
The CGAL Project · 2015
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On the topology of random complexes built over stationary point processes
D. Yogeshwaran, Robert J. Adler, and others · 2015
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