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