Two Point Correlation Functions for a Periodic Box-Ball System

Jun Mada^a, Tetsuji Tokihiro<sup>b

a</sup> College of Industrial Technology, Nihon University, 2-11-1 Shin-ei, Narashino, Chiba 275-8576, Japan
^b Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Tokyo 153-8914, Japan

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.

Keywords: correlation function; box-ball system.

MSC: 37B15; 37K10; 81R12; 82B20

Received: December 13, 2010; in final form March 2, 2011; Published online March 21, 2011

Language: English

DOI: 10.3842/SIGMA.2011.027

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ArXiv: 1103.3929