Exponential decay of correlations for a real-valued dynamical system generated by a k dimensional system

TL;DR

This paper investigates the decay of correlations in a real-valued dynamical system generated by a k-dimensional recurrence relation, establishing decay results under analytic conditions on the defining function.

Contribution

It provides new theoretical results on correlation decay for systems defined by analytic recurrence relations, extending understanding of their long-term statistical behavior.

Findings

Proves decay of correlations under analytic hypotheses

Establishes conditions for exponential decay in k-dimensional systems

Advances theoretical understanding of recurrence relation dynamics

Abstract

We study the real, bounded-variables process (X_n) defined by a k-term recurrence relation X_{n+k} ={\phi}(X_n, ... , X_{n+k-1}). We prove the decay of correlations, mainly under purely analytic hypotheses concerning the function {\phi} and its partial derivatives.