Semicircle Law of Vandermonde Ensemble
Da Xu, Lihe Wang
TL;DR
This paper provides a straightforward proof of the level density for the fixed trace square ensemble, deriving an integral equation and analyzing its asymptotic behavior to understand the semicircle law in this context.
Contribution
It introduces a simple proof and integral equation for the level density of the fixed trace square ensemble, advancing understanding of its asymptotic properties.
Findings
Confirmed semicircle law for the ensemble
Derived integral equation for level density
Analyzed asymptotic behavior of the density
Abstract
In the present paper, we give a simple proof of the level density of fixed trace square ensemble.We derive the integral equation of the level density of fixed trace square ensemble.Then we analyze the asymptotic behavior of the level density.
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Taxonomy
TopicsRandom Matrices and Applications · Stochastic processes and statistical mechanics · Theoretical and Computational Physics