Extreme Value Laws for sequences of intermittent maps

TL;DR

This paper establishes Extreme Value Laws for non-stationary processes generated by sequential dynamical systems with neutral fixed points, extending previous work to more general non-uniformly mixing maps.

Contribution

It generalizes the theory of extreme values to non-stationary processes from maps with neutral fixed points, weakening mixing conditions.

Findings

Proves existence of Extreme Value Laws for these processes.

Extends previous results from uniformly expanding maps to maps with neutral fixed points.

Provides a broader framework for analyzing extreme values in non-stationary dynamical systems.

Abstract

We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed points and prove the existence of Extreme Value Laws for such processes. We use an approach developed in \cite{FFV16}, where we generalised the theory of extreme values for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. The present work is an extension of our previous results for concatenations of uniformly expanding maps obtained in \cite{FFV16}.