Polynomial rate of mixing for the heterochaos baker maps with mostly neutral center

TL;DR

This paper proves that certain heterochaos baker maps with mostly neutral centers exhibit an optimal polynomial decay of correlations at a rate of n^{-3/2}, using a novel comparison to gambler's ruin problem.

Contribution

It introduces a new method to analyze decay of correlations in heterochaos baker maps with neutral centers by relating it to gambler's ruin problem.

Findings

Correlations decay at rate n^{-3/2} for the studied maps.

Method relies on Perron-Frobenius operator comparison to gambler's ruin.

Optimal polynomial decay established for maps with mostly neutral centers.

Abstract

For the heterochaos baker maps whose central direction is mostly neutral, we prove that correlations for H\"older continuous functions decay at an optimal polynomial rate of order $n^{-3/2}$. Our method of proof relies on a description of the action of a reduced Perron-Frobenius operator by means of a comparison to the symmetric simple random walk with an absorbing wall, aka `gambler's ruin problem'.