Journal article

Global and local scaling limits for the β = 2 Stieltjes-Wigert random matrix ensemble

PJ Forrester

Random Matrices: Theory and Application | World Scientific Pub Co Pte Lt | Published : 2021

Abstract

The eigenvalue probability density function (PDF) for the Gaussian unitary ensemble has a well-known analogy with the Boltzmann factor for a classical log-gas with pair potential -log |x - y|, confined by a one-body harmonic potential. A generalization is to replace the pair potential by -log |sinh(π(x - y)/L)|. The resulting PDF first appeared in the statistical physics literature in relation to non-intersecting Brownian walkers, equally spaced at time t = 0, and subsequently in the study of quantum many-body systems of the Calogero-Sutherland type, and also in Chern-Simons field theory. It is an example of a determinantal point process with correlation kernel based on the Stieltjes-Wigert ..

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