Tsukuba Journal of Mathematics

Derivation of Wigner's semi-circle law for a class of matrix ensembles via Brownian motion

Tsuyoshi Hiratsuka and Nariyuki Minami

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Abstract

Introducing a fictitious time evolution in a random matrix model having Gaussian entries, we prove that the empirical distribution of the scaled eigenvalues of the random matrix converges in probability to the Wigner's semi-circle law.

Article information

Source
Tsukuba J. Math., Volume 25, Number 2 (2001), 443-464.

Dates
First available in Project Euclid: 30 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1496164298

Digital Object Identifier
doi:10.21099/tkbjm/1496164298

Mathematical Reviews number (MathSciNet)
MR1869773

Zentralblatt MATH identifier
1007.60085

Citation

Hiratsuka, Tsuyoshi; Minami, Nariyuki. Derivation of Wigner's semi-circle law for a class of matrix ensembles via Brownian motion. Tsukuba J. Math. 25 (2001), no. 2, 443--464. doi:10.21099/tkbjm/1496164298. https://projecteuclid.org/euclid.tkbjm/1496164298


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