Landscape dynamics, interbasin kinetics and ultrametric diffusion

TL;DR

This paper explores how random walks on complex landscapes can be approximated by ultrametric diffusion processes, revealing a mathematical equivalence with p-adic heat equations and providing insights into landscape dynamics.

Contribution

It establishes a theoretical link between interbasin kinetics and ultrametric diffusion, introducing a novel ultrametric pseudodifferential operator framework.

Findings

Interbasin kinetics approximates random walks on complex landscapes.

Ultrametric diffusion is generated by an ultrametric pseudodifferential operator.

The p-adic heat equation exemplifies ultrametric diffusion.

Abstract

We discuss the interbasin kinetics approximation for random walk on a complex landscape. We show that for a generic landscape the corresponding model of interbasin kinetics is equivalent to an ultrametric diffusion, generated by an ultrametric pseudodifferential operator on the ultrametric space related to the tree of basins. The simplest example of ultrametric diffusion of this kind is described by the p-adic heat equation.