Examples of stable-like random walks on groups of polynomial growth

2025/08/31 by Laurent Saloff‐Coste, Saloff-Coste, Laurent, Zhang, Ruoqi · 1 citation
Mathematics · #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2509.00970

openalex publication_date 2025/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider several families of long jump random walks on groups of polynomial volume growth which are naturally expected to have a stable-like behavior. We then prove optimal pseudo-Poincaré inequalities for these walks. These pseudo-Poincaré inequalities allow us to show that the random walks in questions indeed have a stable-like behavior and to obtain detailed estimates.

Citations

• Limit theorems for some long range random walks on torsion free nilpotent groups
• Long range random walks and associated geometries on groups of polynomial growth
• Random walks under slowly varying moment conditions on groups of polynomial volume growth
• Random walks on nilpotent groups driven by measures supported on powers of generators

Cited by

• Comparison of Dirichlet forms for stable-like random walks on groups of polynomial volume growth

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• Random walks under slowly varying moment conditions on groups of polynomial volume growth
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