Spectral analysis of a semiclassical random walk associated to a general confining potential

2024/01/23 by Thomas Normand, Normand, Thomas
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2401.12765

openalex publication_date 2024/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider a semiclassical random walk with respect to a probability measure associated to a potential with a finite number of critical points. We recover the spectral results from [1] on the corresponding operator in a more general setting and with improved accuracy. In particular we do not make any assumption on the distribution of the critical points of the potential, in the spirit of [15]. Our approach consists in adapting the ideas from [15] to the recent gaussian quasimodes framework which appears to be more robust than the usual methods, especially when dealing with non local operators.

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