The Pillowcase Distribution and Near-Involutions

TL;DR

This paper advances the understanding of pillowcase weight distributions and near-involutions, providing new results that clarify difficulties and simplify proofs in the context of moduli space volume calculations.

Contribution

It introduces new findings on pillowcase distributions and near-involutions, enhancing the theoretical framework for moduli space volume computations.

Findings

New results on pillowcase weight distributions

Simplified proofs of existing theorems

Insights into asymptotic characters of near-involutions

Abstract

In the context of the Eskin-Okounkov approach to the calculation of the volumes of the different strata of the moduli space of quadratic differentials, the important ingredients are the pillowcase weight probability distribution on the space of Young diagrams, and the asymptotic study of characters of permutations that near-involutions. In this paper we present various new results for these objects. Our results give light to unforeseen difficulties in the general solution to the problem, and they simplify some of the previous proofs.