Local central limit theorem for Mallows measure

2024/09/16 by Alexey Bufetov, Bufetov, Alexey, Kailun Chen +1
Mathematics · Economics, Econometrics and Finance · #Point processes and geometric inequalities #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2409.10415

Abstract

We study the statistics of the Mallows measure on permutations in the limit pioneered by Starr (2009). Our main result is the local central limit theorem for its height function. We also re-derive versions of the law of large numbers and the large deviation principle, obtain the standard central limit theorem from the local one, and establish a multi-point version of the local central limit theorem.

Related

• Limit Theorems for the Length of the Longest Common Subsequence of Mallows Permutations
• Classical patterns in Mallows permutations
• A central limit theorem for a new statistic on permutations
• The global and local limit of the continuous-time Mallows process
• A central limit theorem for cycles of Mallows permutations