Work

Local limit theorems for random walks on nilpotent Lie groups

Year: 2025

Type: article

Abstract: We establish the (non-lattice) local limit theorem for products of i.i.d. random variables on an arbitrary simply connected nilpotent Lie group G, where the variables are allowed to be non-centered. Our result also improves on the known centered case by proving uniformity for two-sided moderate deviations and allowing measures with a moment of order $$2(\dim G)^2$$ without further regularity assumptions. As applications we establish a Ratner-type equidistribution theorem for unipotent walks on homogeneous spaces and obtain a new proof of the Choquet-Deny property in our setting.

Source: Probability Theory and Related Fields

DOI: 10.1007/s00440-025-01387-4

Authors: Timothée Bénard, Emmanuel Breuillard

Institutions: Centre National de la Recherche Scientifique, Université Sorbonne Paris Nord, Laboratoire Analyse, Géométrie et Applications, University of Oxford

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: European Commission