A factorization of determinant related to some random matrices

Tomoyuki Shirai

doi:10.1023/a:1023252000178

A factorization of determinant related to some random matrices

Tomoyuki Shirai

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We consider the expectation of the determinant del(λ - X)^-1 for Im λ > 0 associated with some random NxN matrices and factorize it into N Stieltjes transforms of probability measures. Moreover, using this factorization, we investigate the limiting behavior of the logarithm of the quantity as N → ∞.

Original language	English
Pages (from-to)	1449-1459
Number of pages	11
Journal	Journal of Statistical Physics
Volume	90
Issue number	5-6
DOIs	https://doi.org/10.1023/a:1023252000178
Publication status	Published - Mar 1998
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1023/a:1023252000178

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title = "A factorization of determinant related to some random matrices",

abstract = "We consider the expectation of the determinant del(λ - X)-1 for Im λ > 0 associated with some random NxN matrices and factorize it into N Stieltjes transforms of probability measures. Moreover, using this factorization, we investigate the limiting behavior of the logarithm of the quantity as N → ∞.",

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AB - We consider the expectation of the determinant del(λ - X)-1 for Im λ > 0 associated with some random NxN matrices and factorize it into N Stieltjes transforms of probability measures. Moreover, using this factorization, we investigate the limiting behavior of the logarithm of the quantity as N → ∞.

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A factorization of determinant related to some random matrices

Abstract

All Science Journal Classification (ASJC) codes

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