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We prove an analogue of Alon's spectral gap conjecture for random bipartite, biregular graphs.
Low-density parity-check codes
R. Gallager · 1962
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The asymptotic number of non-negative integer matrices with given row and column sums
Edward A. Bender · 1974
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The asymptotic number of labeled graphs with given degree sequences
Edward A Bender and E. Rodney Canfield · 1978
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A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs
Béla Bollobás · 1980
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Subgraphs of random graphs with specified degrees
Brendan D McKay · 1981
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A recursive approach to low complexity codes
R. Tanner · 1981
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The asymptotic connectivity of labelled regular graphs
Nicholas C. Wormald · 1981
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Stochastic blockmodels: First steps
Paul W. Holland, Kathryn Blackmond Laskey, and Samuel Leinhardt · 1983
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Asymptotics for 0-1 Matrices with Prescribed Line Sums
Brendan D McKay · 1984
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Eigenvalues and expanders
Noga Alon · 1986
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Walk generating functions and spectral measures of infinite graphs
C. D. Godsil and B. Mohar · 1988
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The Ihara-Selberg zeta function of a tree lattice
Hyman Bass · 1992
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Spectra of Regular Graphs and Hypergraphs and Orthogonal Polynomials
Wen-Ch’ing Winnie Li and Patrick Solé · 1996
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Zeta Functions of Finite Graphs
Motoko Kotani and Toshikazu Sunada · 2000
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Random Graphs
Béla Bollobás · 2001
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Relative expanders or weakly relatively Ramanujan graphs
Joel Friedman · 2003
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On Tanner Codes: Minimum Distance and Decoding
H. Janwa and A. K. Lal · 2003
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The semicircle law for semiregular bipartite graphs
Hirobumi Mizuno and Iwao Sato · 2003
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The renaissance of Gallager’s low-density parity-check codes
T. Richardson and R. Urbanke · 2003
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A proof of Alon’s second eigenvalue conjecture and related problems
Joel Friedman · 2004
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Rank, Trace-Norm and Max-Norm
Nathan Srebro and Adi Shraibman · 2005
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Maximum-Margin Matrix Factorization
Nathan Srebro, Jason Rennie, and Tommi S. Jaakkola · 2005
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Shlomo Hoory, Nathan Linial, and Avi Wigderson · 2006
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The Non-Backtracking Spectrum of the Universal Cover of a Graph
Omer Angel, Joel Friedman, and Shlomo Hoory · 2007
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Complexity measures of sign matrices
Nati Linial, Shahar Mendelson, Gideon Schechtman, and Adi Shraibman · 2007
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The rank of random graphs
Kevin P. Costello and Van H. Vu · 2008
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The non-backtracking spectrum of the universal cover of a graph
Omer Angel, Joel Friedman, and Shlomo Hoory · 2014
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Universal Matrix Completion
Srinadh Bhojanapalli and Prateek Jain · 2014
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The Relativized Second Eigenvalue Conjecture of Alon
Joel Friedman and David-Emmanuel Kohler · 2014
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Deterministic algorithms for matrix completion
Eyal Heiman, Gideon Schechtman, and Adi Shraibman · 2014
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Equitable random graphs
M. E. J. Newman and Travis Martin · 2014
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A new proof of Friedman’s second eigenvalue Theorem and its extension to random lifts
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A Direct Product Theorem for Discrepancy
Troy Lee, Adi Shraibman, and Robert Špalek · 2008
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Modern Coding Theory
Tom Richardson and Ruediger Urbanke · 2008
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Matrix Completion With Noise
E. J. Candes and Y. Plan · 2009
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Community detection in graphs
Santo Fortunato · 2009
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Graph zeta function in the bethe free energy and loopy belief propagation
Yusuke Watanabe and Kenji Fukumizu · 2009
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Resolvent of large random graphs
Charles Bordenave and Marc Lelarge · 2010
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Charles Bordenave · 2015
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Non-backtracking spectrum of random graphs: Community detection and non-regular Ramanujan graphs
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Recovery and Rigidity in a Regular Stochastic Block Model
Gerandy Brito, Ioana Dumitriu, Shirshendu Ganguly, Christopher Hoffman, and Linh V. Tran · 2015
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Anti-concentration property for random digraphs and invertibility of their adjacency matrices
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A class of network models recoverable by spectral clustering
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Equitable decompositions of graphs with symmetries
Wayne Barrett, Amanda Francis, and Benjamin Webb · 2016
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Recovery and Rigidity in a Regular Stochastic Block Model
Gerandy Brito, Ioana Dumitriu, Shirshendu Ganguly, Christopher Hoffman, and Linh V. Tran · 2016
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The Marčenko-Pastur law for sparse random bipartite biregular graphs
Ioana Dumitriu and Tobias Johnson · 2016
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Non-Backtracking Random Walks and a Weighted Ihara’s Theorem
Mark Kempton · 2016
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Adjacency matrices of random digraphs: Singularity and anti-concentration
Alexander E. Litvak, Anna Lytova, Konstantin Tikhomirov, Nicole Tomczak-Jaegermann, and Pierre Youssef · 2016
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Spectral partitioning in equitable graphs
Paolo Barucca · 2017
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The Spectral Gap of Sparse Random Digraphs
Simon Coste · 2017
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Matrix Completion from $O(n)$ Samples in Linear Time
David Gamarnik, Quan Li, and Hongyi Zhang · 2017
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The threshold for SDP-refutation of random regular NAE-3SAT
Yash Deshpande, Andrea Montanari, Ryan O’Donnell, Tselil Schramm, and Subhabrata Sen · 2018
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On the singularity of adjacency matrices for random regular digraphs
Nicholas A. Cook · 2064
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