Strong convergence of tensor products of independent G.U.E. matrices

2022/05/16 by Belinschi, Serban, Capitaine, Mireille · 2 citations
#FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2205.07695

Abstract

Given tuples of properly normalized independent N× N G.U.E. matrices (X_N⁽¹⁾,…,X_N^(r₁)) and (Y_N⁽¹⁾,…,Y_N^(r₂)), we show that the tuple (X_N⁽¹⁾⊗ I_N,…,X_N^(r₁)⊗ I_N,I_N⊗ Y_N⁽¹⁾,…,I_N⊗ Y_N^(r₂)) of N²× N² random matrices converges strongly as N tends to infinity. It was shown by Ben Hayes that this result implies that the Peterson-Thom conjecture is true.

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