About universality of large deviation principles for conjugacy invariant permutations

TL;DR

This paper demonstrates that large deviation principles are universal for conjugacy invariant permutations with few cycles, including Ewens measures, and applies this to the length of monotone subsequences.

Contribution

It establishes the universality of large deviations for conjugacy invariant permutations, extending known results to a broader class including Ewens measures.

Findings

Large deviations hold universally for permutations with few cycles.

Universality applies to speeds n and √n for monotone subsequences.

Provides sharp control over the total number of cycles.

Abstract

We prove the universality of the large deviations for conjugacy invariant permutations with few cycles. As an application, we establish the universality of large deviation at speeds $n$ and $\sqrt{n}$ for the length of monotone subsequences in conjugacy invariant permutations, with a sharp control over the total number of cycles. This universality class includes the well-known Ewens measures.