Circular law for random matrices with exchangeable entries
type: Dataset
description: An exchangeable random matrix is a random matrix with distribution invariant under any permutation of the entries. For such random matrices, we show, as the dimension tends to infinity, that the empirical spectral distribution tends to the uniform law on the unit disc. This is an instance of the universality phenomenon known as the circular law, for a model of random matrices with dependent entries, rows, and columns. It is also a non-Hermitian counterpart of a result of Chatterjee on the semi-circular law for random Hermitian matrices with exchangeable entries. The proof relies in particular on a reduction to a simpler model given by a random shuffle of a rigid deterministic matrix, on Hermitization, and also on combinatorial concentration of measure and combinatorial Central Limit Theorem. A crucial step is a polynomial bound on the smallest singular value of exchangeable random matrices, which may be of independent interest.
issued: 2026-05-06T09:21:03.679847
language: en
modified: 2026-05-06T09:21:03.679853
contact point: Organization
  fn: CCSD
keyword: 05c80--60b20
keyword: combinatorial-central-limit-theorem
keyword: concentration-of-measure
keyword: exchangeable-distributions
keyword: infoeu-reposemanticsarticle
keyword: journal-articles
keyword: mathmath-prmathematics-mathprobability-mathpr
keyword: random-matrices
keyword: random-permutations
keyword: smallest-singular-value
keyword: spectral-analysis
landing page: 1042-9832

Circular law for random matrices with exchangeable entries
type: Distribution
format: HTML
issued: 2026-05-06T09:21:03.705746
modified: 2026-05-06T09:21:03.664868
access URL: https://hal.science/hal-00947145

test_moissonnage_selune
type: Agent