Asset Details
Do you wish to reserve the book?
Involution factorizations of Ewens random permutations
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
Involution factorizations of Ewens random permutations
Do you wish to request the book?
Involution factorizations of Ewens random permutations
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
Involution factorizations of Ewens random permutations
2025
Overview
An involution is a bijection that is its own inverse. Given a permutation $σ$ of $[n],$ let $\\mathsf{invol}(σ)$ denote the number of ways $σ$ can be expressed as a composition of two involutions of $[n].$ We prove that the statistic $\\mathsf{invol}$ is asymptotically lognormal when the symmetric groups $\\mathfrak{S}_n$ are each equipped with Ewens Sampling Formula probability measures of some fixed positive parameter $θ.$ This paper strengthens and generalizes previously determined results about the limiting distribution of $\\log(\\mathsf{invol})$ for uniform random permutations, i.e. the specific case of $θ= 1$. We also investigate the first two moments of $\\mathsf{invol}$ itself, detailing the phase transition in asymptotic behavior at $θ= 1,$ and provide a functional refinement and a convergence rate for the Gaussian limit law which is demonstrably optimal when $θ= 1.$
Publisher
Discrete Mathematics & Theoretical Computer Science
Subject
