Correlation function for a periodic box-ball system

TL;DR

This paper derives explicit formulas for correlation functions in a periodic box-ball system, using combinatorial methods and ultradiscrete theta functions, advancing understanding of its statistical properties.

Contribution

It provides the first explicit combinatorial formulas for short-distance two-point functions and general N-point functions in periodic box-ball systems.

Findings

Explicit formulas for two-point functions at short distances

Expressions for general N-point functions using ultradiscrete theta functions

Enhanced analytical tools for studying periodic box-ball systems

Abstract

We investigate correlation functions in a periodic box-ball system. For the two point functions of short distance, we give explicit formulae obtained by combinatorial methods. We give expressions for general N-point functions in terms of ultradiscrete theta functions.