Two Point Correlation Functions for a Periodic Box-Ball System

TL;DR

This paper derives explicit formulas and recursion relations for correlation functions in a periodic box-ball system, advancing the understanding of its statistical properties through combinatorial methods.

Contribution

It provides new explicit formulas and recursion relations for correlation functions in the periodic box-ball system, which were not previously available.

Findings

Explicit formulas for second and third nearest neighbor correlations.

A recursion formula for N-point correlation functions.

Enhanced understanding of the system's statistical structure.

Abstract

We investigate correlation functions in a periodic box-ball system. For the second and the third nearest neighbor correlation functions, we give explicit formulae obtained by combinatorial methods. A recursion formula for a specific $N$-point functions is also presented.