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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Large n Limit for the Product of Two Coupled Random Matrices

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Author(s):
Silva, Guilherme L. F. [1] ; Zhang, Lun [2, 3]
Total Authors: 2
Affiliation:
[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Ave Trabalhador Sao Carlense 400, BR-13566590 Sao Carlos, SP - Brazil
[2] Fudan Univ, Sch Math Sci, Shanghai 200433 - Peoples R China
[3] Fudan Univ, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433 - Peoples R China
Total Affiliations: 3
Document type: Journal article
Source: Communications in Mathematical Physics; v. 377, n. 3 JUN 2020.
Web of Science Citations: 0
Abstract

For a pair of coupled rectangular random matrices we consider the squared singular values of their product, which form a determinantal point process. We show that the limiting mean distribution of these squared singular values is described by the second component of the solution to a vector equilibrium problem. This vector equilibrium problem is defined for three measures with an upper constraint on the first measure and an external field on the second measure. We carry out the steepest descent analysis for a 4 x 4 matrix-valued Riemann-Hilbert problem, which characterizes the correlation kernel and is related to mixed type multiple orthogonal polynomials associated with the modified Bessel functions. A careful study of the vector equilibrium problem, combined with this asymptotic analysis, ultimately leads to the aforementioned convergence result for the limiting mean distribution, an explicit form of the associated spectral curve, as well as local Sine, Meijer-G and Airy universality results for the squared singular values considered. (AU)

FAPESP's process: 19/16062-1 - Asymptotic analysis of interacting particle systems and random matrix theory
Grantee:Guilherme Lima Ferreira da Silva
Support Opportunities: Research Grants - Young Investigators Grants
FAPESP's process: 20/02506-2 - Asymptotic analysis of interacting particle systems and random matrix theory
Grantee:Guilherme Lima Ferreira da Silva
Support Opportunities: Scholarships in Brazil - Young Researchers