Some classes of non-archimedean radial probability density functions associated with energy landscapes

TL;DR

This paper explores a broad class of p-adic radial probability densities linked to energy landscapes, developing associated pseudo-differential operators, analyzing heat kernels, and studying stochastic processes relevant to complex systems.

Contribution

It introduces new classes of non-archimedean radial probability densities and analyzes their properties, including heat kernels and Markov processes, in the context of energy landscapes.

Findings

Properties of heat kernels for p-adic pseudo-differential operators

Analysis of fundamental solutions of p-adic equations

Study of Markov processes and first passage times in energy landscapes

Abstract

In this article, we study a large class of radial probability density functions defined on the p-adic numbers from which it is possible to obtain certain non-archimedean pseudo-differential operators. These operators are associated with certain p-adic master equations of some models of complex systems (such as glasses, macromolecules, and proteins). We prove via the theory of distributions some properties corresponding to the heat Kernel associated with these pseudo-differential operators. Also, study some properties corresponding to the fundamental solution of these p-adic equations. Finally, we will study strong Markov processes, the first passage time problem and the survival probability (of the trajectories of these processes) corresponding to radial probability density functions connected with energy landscapes of the linear and logarithmic types.