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Combinatorics and loop equations for antisymmetrised and Hermitised matrix product ensembles
Stephane Dartois, Anas. A Rahman
The order antisymmetrised matrix product ensemble is represented by the product , where are independent real Ginibre matrices…
Equivalence of Fixed-Rank and Rank-One Even-Order Symmetric Tensor Factorization
Ruba Hussen Morsi, Anas A. Rahman
In the recent work of Barbier, Ko, and the second present author on sublinear-rank symmetric matrix factorization [Math. Stat. Learn. 9 (2026), 1-68], a key result is that, in the…
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…