About universality of large deviation principles for conjugacy invariant permutations

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.

Cited by in corpus (1)

• A geometric approach to conjugation-invariant random permutations