Hitting times distribution and extreme value law for flows

TL;DR

This paper investigates the distribution of hitting times and extreme values in flows with mixing properties, establishing exponential limit laws and linking them to extreme value distributions, especially for systems modeled by Young's tower.

Contribution

It generalizes previous results by connecting hitting time distributions and extreme value laws for flows, including those modeled by Young's tower with polynomial tails.

Findings

Hitting time distribution converges to exponential in limit.

Extreme value law is established for flows with certain mixing properties.

Results extend to systems modeled by Young's tower with polynomial tail.

Abstract

For flows whose return map on a cross section has sufficient mixing property, we show that the hitting time distribution of the flow to balls is exponential in limit. We also establish a link between the extreme value distribution of the flow and its hitting time distribution, generalizing a previous work by Freitas et al. in the discrete time case. Finally we show that for maps that can be modeled by Young`s tower with polynomial tail, the extreme value law holds.