Non-Degenerate Ultrametric Diffusion

TL;DR

This paper introduces a class of non-degenerate p-adic ultrametric diffusion operators, constructs their eigenvector bases, computes eigenvalues, and explores the properties of the resulting ultrametric diffusion dynamics.

Contribution

It presents new non-degenerate p-adic ultrametric diffusion operators, along with their eigenstructure and dynamic properties, advancing the mathematical understanding of ultrametric processes.

Findings

Eigenvector bases constructed for the operators

Eigenvalues explicitly computed

Properties of ultrametric diffusion dynamics analyzed

Abstract

General non-degenerate p-adic operators of ultrametric diffusion are introduced. Bases of eigenvectors for the introduced operators are constructed and the corresponding eigenvalues are computed. Properties of the corresponding dynamics (i.e. of the ultrametric diffusion) are investigated.