Short cycles of random permutations with cycle weights: Point processes approach

Galganov, Oleksii; Ilienko, Andrii (2024). Short cycles of random permutations with cycle weights: Point processes approach. Statistics & Probability Letters, 213 Elsevier 10.1016/j.spl.2024.110169

	Text Cycles.pdf - Accepted Version Restricted to registered users only until 1 June 2026. Available under License Publisher holds Copyright. Download (474kB)
	Text 1-s2.0-S016771522400138X-main.pdf - Published Version Restricted to registered users only Available under License Publisher holds Copyright. Download (561kB)

We study the asymptotic behavior of short cycles of random permutations with cycle weights. More specifically, on a specially constructed metric space whose elements encode all possible cycles, we consider a point process containing all information on cycles of a given random permutation on 1,…,n. The main result of the paper is the distributional convergence with respect to the vague topology of the above processes towards a Poisson point process as n→∞ for a wide range of cycle weights. As an application, we give several limit theorems for various statistics of cycles.

Interest & Impact

Downloads

4 since deposited on 10 Jun 2024
4 in the past 12 months

Citations

5 Citations in Web of Science ®
6 Citations in Scopus

Search

in Google Scholar™

Services

Actions (login required)

Edit item

Actions (login required)

Edit item