Logarithmic potential theory and large deviation

TL;DR

This paper establishes a broad large deviation principle for probability measures related to random matrix theory, utilizing logarithmic potential theory and contraction principles on unbounded sets in the complex plane.

Contribution

It extends large deviation principles to unbounded sets with weakly admissible external fields and general measures, using advanced potential theory techniques.

Findings

Derived a general large deviation principle for measures on unbounded sets

Applied potential theory and contraction principles in a novel way

Extended results to very general measures and external fields

Abstract

We derive a general large deviation principle for a canonical sequence of probability measures, having its origins in random matrix theory, on unbounded sets $K$ of ${\bf C}$ with weakly admissible external fields $Q$ and very general measures $\nu$ on $K$. For this we use logarithmic potential theory in ${\bf R}^{n}$, $n\geq 2$, and a standard contraction principle in large deviation theory which we apply from the two-dimensional sphere in ${\bf R}^{3}$ to the complex plane ${\bf C}$.