2017/12/11 by Mihai Popa, Popa, Mihai, Zhiwei Hao +1 · 1 citation
Mathematics · #46L53 #Advanced Algebra and Geometry #Combinatorics (math.CO) #FOS: Mathematics #Operator Algebras (math.OA) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.CO #math.OA #msc:46L53
paper · pdf · doi:10.48550/arxiv.1712.04031
19 pages, no figures
arxiv created 2017/12/11 · openalex publication_date 2017/12/11 · arxiv updated 2017/12/13 · openalex created_date 2017/12/22 · openalex updated_date 2026/07/28
Motivated by the recent work on asymptotic independence relations for random matrices with non-commutative entries, we investigate the limit distribution and independence relations for large matrices with identically distributed and Boolean independent entries. More precisely, we show that, under some moment conditions, such random matrices are asymptotically B -diagonal and Boolean independent from each other. The paper also gives a combinatorial condition under which such matrices are asymptotically Boolean independent from the matrix obtained by permuting the entries (thus extending a recent result in Boolean probability). In particular, we show that random matrices considered are asymptotically Boolean independent from their partial transposes. The main results of the paper are based on combinatorial techniques.