4 papers
A contiguity approach to replica symmetric marginals
Ernesto Mordecki, Anas A. Rahman, Manuel Sáenz
We develop a probabilistic cavity-contiguity framework for proving replica-symmetric convergence of local marginals in mean-field Gibbs systems. The approach is based on cavity dec…
Edge density expansions for the classical Gaussian and Laguerre ensembles
Peter J. Forrester, Anas A. Rahman, Bo-Jian Shen
Recent work of Bornemann has uncovered hitherto hidden integrable structures relating to the asymptotic expansion of quantities at the soft edge of Gaussian and Laguerre random mat…
A multiscale cavity method for sublinear-rank symmetric matrix factorization
Jean Barbier, Justin Ko, Anas A. Rahman
We consider a statistical model for symmetric matrix factorization with additive Gaussian noise in the high-dimensional regime, where the rank of the signal matrix to infer sca…
Corrections to Classical Matrix Ensemble Moments, Non-Crossing Annular Pairings, and Ribbon Graphs
Anas A. Rahman, Daniel Munoz George, James A. Mingo
We elucidate a bijection between ribbon graphs on the real projective plane and non-crossing annular pairings that relate to the correction term of the GOE and LOE spectral m…