The sojourn time problem for a p-adic random walk and its applications to the spectral diffusion of proteins

2022/06/10 by A. Kh. Bikulov, A. P. Zubarev, Bikulov, A. Kh. +1
Mathematics · #35S05 #60J76 #82C44 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2206.04884

openalex publication_date 2022/06/10 · openalex created_date 2022/06/14 · openalex updated_date 2026/07/28

Abstract

We consider the problem of the distribution of the sojourn time in a compact set ℤ_p in the case of a p-adic random walk. We rely on the results of our previous studies of the distribution of the first return time for a p-adic random walk and the results of Takacs on the study of the sojourn time problem for a wide class of random processes. For a p-adic random walk we find the mean sojourn time of the trajectory in ℤ_p and the asymptotics as t→∞ of arbitrary moments of the distribution of the sojourn time in ℤ_p. We also discuss some possible applications of our results to the modeling of relaxation processes related to the conformational dynamics of protein.

Related

• Model of the p-Adic Random Walk in a Potential
• Oscillations in p-adic diffusion processes and simulation of the conformational dynamics of protein
• Brownian Motion in the p-Adic Integers is a Limit of Discrete Time Random Walks
• Random walk with heterogeneous sojourn time
• Classical first passage problems for p-adic stochastic processes