Asymptotic behavior and moderate deviation principle for the maximum of a Dyck path

TL;DR

This paper establishes large and moderate deviation principles for the maximum height of a random Dyck path, extending previous results in the field.

Contribution

It introduces new deviation principles for Dyck path maxima, broadening the understanding of their asymptotic behavior.

Findings

Large deviation principle for Dyck path maximum

Moderate deviation principle for Dyck path maximum

Extension of previous deviation results

Abstract

In this paper, we obtain a large and moderate deviation principle for the law of the maximum of a random Dyck path. Our result extend the results of Chung, Kennedy, Kaigh and Khorunzhiy and Marckert.