Wigner Surmise For Domain Systems

TL;DR

This paper investigates the application of the Wigner surmise approximation to non-equilibrium systems, providing a new analytical approach to their statistical behavior, exemplified by the annihilation random walk.

Contribution

It extends the Wigner surmise approximation from random matrix theory to complex non-equilibrium systems, offering a novel analytical tool.

Findings

Wigner surmise approximates spacing distributions in non-equilibrium systems

Provides analytical approximation for annihilation random walk

Demonstrates the approach's potential for complex system analysis

Abstract

In random matrix theory, the spacing distribution functions $p^{(n)}(s)$ are well fitted by the Wigner surmise and its generalizations. In this approximation the spacing functions are completely described by the behavior of the exact functions in the limits s->0 and s->infinity. Most non equilibrium systems do not have analytical solutions for the spacing distribution and correlation functions. Because of that, we explore the possibility to use the Wigner surmise approximation in these systems. We found that this approximation provides a first approach to the statistical behavior of complex systems, in particular we use it to find an analytical approximation to the nearest neighbor distribution of the annihilation random walk.