Components and Exit Times of Brownian Motion in two or more p-Adic Dimensions

2022/10/28 by Rahul Rajkumar, Rajkumar, Rahul, David Weisbart +1 · 4 citations
Mathematics · #26E30 (secondary) #60G22 (primary) #FOS: Mathematics #Probability (math.PR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2210.16429

openalex publication_date 2022/10/28 · openalex created_date 2022/11/06 · openalex updated_date 2026/07/28

Abstract

The fundamental solution of a pseudo-differential equation for functions defined on the d-fold product of the p-adic numbers, ℚ_p, induces an analogue of the Wiener process in ℚ_p^d. As in the real setting, the components are 1-dimensional p-adic Brownian motions with the same diffusion constant and exponent as the original process. Asymptotic analysis of the conditional probabilities shows that the vector components are dependent for all time. Exit time probabilities for the higher dimensional processes reveal a concrete effect of the component dependency.

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• Hearing the Serre invariant of a compact p-adic analytic manifold
• Diffusion operators on p-adic analytic manifolds
• Geometry-induced criticality in p-adic scaling limits of random walks
• Vladimirov-Pearson Operators on ζ-regular Ultrametric Cantor Sets

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