Year: 2025
Type: article
Abstract: Continuous-time Mallows processes are processes of random permutations of the set {1,…,n} whose marginal at time t is the Mallows distribution with parameter t. Recently Corsini showed that there exists a unique Markov Mallows process whose left inversions are independent counting processes. We prove that this process admits a global and a local limit as n→∞. The global limit, obtained after suitably rescaling space and time, is an explicit stochastic process on [0,1] whose description is based on the permuton limit of the Mallows distribution, analyzed by Starr. The local limit is a process of permutations of Z which is closely related to the construction of the Mallows distribution on permutations of Z due to Gnedin and Olshanski. Our results demonstrate an analogy between the asymptotic behavior of Mallows processes and the recently studied limiting properties of random sorting networks.
DOI: 10.1214/25-aap2169
Authors: Radosław Adamczak, Michał Kotowski
Institution: University of Warsaw
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4413180689