Transitional random matrix theory nearest-neighbor spacing distributions

TL;DR

This paper introduces a matrix model to describe transitions between Wigner surmises in Random Matrix theory, providing new analytical expressions and approximations for the resulting spacing distributions.

Contribution

It offers the first closed-form analytical expressions for transitional spacing distributions in Random Matrix theory, advancing understanding of spectral transitions.

Findings

Derived exact analytical expressions for transitional distributions

Developed analytical approximations for complex cases

Enhanced modeling of spectral transitions in RMT

Abstract

This paper presents a study of the properties of a matrix model that was introduced to describe transitions between all Wigner surmises of Random Matrix theory. New results include closed-form exact analytical expressions for the transitional probability density functions, as well as suitable analytical approximations for cases not amenable to explicit representation.