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We study the problem of detecting latent geometric structure in random graphs.
Note on the gamma function
JG Wendel · 1948
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The distribution of distance in a hypersphere
John M Hammersley · 1950
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Some Continuous Monte Carlo Methods for the Dirichlet Problem
Mervin E Muller · 1956
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On random graphs I
Paul Erdős and Alfréd Rényi · 1959
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A note on a method for generating points uniformly on n-dimensional spheres
Mervin E Muller · 1959
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Choosing a point from the surface of a sphere
George Marsaglia · 1972
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Cliques in random graphs
Béla Bollobás and Paul Erdős · 1976
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On some inequalities for the gamma and psi functions
Horst Alzer · 1997
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The capacity of wireless networks
Piyush Gupta and Panganmala R Kumar · 2000
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Latent space approaches to social network analysis
Peter D Hoff, Adrian E Raftery, and Mark S Handcock · 2002
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Random Geometric Graphs , volume 5
Mathew Penrose · 2003
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Pattern Recognition and Machine Learning
Christopher M Bishop · 2006
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High-dimensional random geometric graphs and their clique number
Luc Devroye, András György, Gábor Lugosi, and Frederic Udina · 2011
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Consistent latent position estimation and vertex classification for random dot product graphs
Daniel L Sussman, Minh Tang, and Carey E Priebe · 2013
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T Tony Cai, Tengyuan Liang, and Harrison H Zhou · 2015
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Approximation of Rectangular Beta-Laguerre Ensembles and Large Deviations
Tiefeng Jiang and Danning Li · 2015
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Statistical mechanics of random geometric graphs: Geometry-induced first-order phase transition
Massimo Ostilli and Ginestra Bianconi · 2015
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Entropic CLT and phase transition in high-dimensional Wishart matrices
Sébastien Bubeck and Shirshendu Ganguly · 2016
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Statistical Inference on Random Dot Product Graphs: a Survey
Avanti Athreya, Donniell E Fishkind, Minh Tang, Carey E Priebe, Youngser Park, Joshua T Vogelstein, Keith Levin, Vince Lyzinski, Yichen Qin, and Daniel L Sussman · 2018
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Phase Transitions in Spatial Networks as a Model of Cellular Symbiosis
Philip Tee and Allan Balmain · 2018
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Latent Distance Estimation for Random Geometric Graphs
Ernesto Araya and Yohann De Castro · 2019
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The middle-scale asymptotics of Wishart matrices
Didier Chételat and Martin T Wells · 2019
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A smooth transition from Wishart to GOE
Miklós Z Rácz and Jacob Richey · 2019
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The geometry of continuous latent space models for network data
Anna L Smith, Dena M Asta, and Catherine A Calder · 2019
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High-dimensional statistics: A non-asymptotic viewpoint , volume 48
Martin J Wainwright · 2019
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Phase transitions for detecting latent geometry in random graphs
Matthew Brennan, Guy Bresler, and Dheeraj Nagaraj · 2020
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Information and dimensionality of anisotropic random geometric graphs
Ronen Eldan and Dan Mikulincer · 2020
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Community detection and percolation of information in a geometric setting
Ronen Eldan, Dan Mikulincer, and Hester Pieters · 2020
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Connectivity in one-dimensional soft random geometric graphs
Michael Wilsher, Carl P Dettmann, and Ayalvadi Ganesh · 2020
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De Finetti-Style Results for Wishart Matrices: Combinatorial Structure and Phase Transitions
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