Decay of correlation for random intermittent maps

TL;DR

This paper investigates how correlations decay in a class of random intermittent maps, showing that the overall decay rate is determined by the map with the fastest relaxation, using Young-tower techniques.

Contribution

It demonstrates that the correlation decay rate for the combined random maps matches that of the fastest relaxing individual map, providing a sharp asymptotic characterization.

Findings

Correlation decay rate is dominated by the fastest relaxing map.

The decay rate for the random system matches the sharp rate of the fastest map.

Young-tower technique effectively analyzes the decay in random intermittent maps.

Abstract

We study a class of random transformations built over finitely many intermittent maps sharing a common indifferent fixed point. Using a Young-tower technique, we show that the map with the fastest relaxation rate dominates the asymptotics. In particular, we prove that the rate of correlation decay for the annealed dynamics of the random map is the same as the sharp rate of correlation decay for the map with the fastest relaxation rate.