Nondegenerate ultrametric diffusion

Non Degenerate Ultrametric Diffusion

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.

, interbasin kinetics and ultrametric diffusion

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 describ...

A diffusion regime with nondegenerate slowdown

We study a diffusion regime, earlier considered by Gurvich, Mandelbaum, Shaikhet and Whitt in the case of the M/M/N queue, that is, in a sense that we make precise, a midpoint between two well-known heavy traffic diffusion regimes, the conventional and the quality and efficiency driven regimes. Unlike the other two, this regime, that we call the non-degenerate slowdown regime, enjoys the proper...

Noncommutative Riemannian Geometry and Diffusion on Ultrametric Cantor Sets

An analogue of the Riemannian Geometry for an ultrametric Cantor set (C, d) is described using the tools of Noncommutative Geometry. Associated with (C, d) is a weighted rooted tree, its Michon tree [28]. This tree allows to define a family of spectral triples (CLip(C),H, D) using the l space of its vertices, giving the Cantor set the structure of a noncommutative Riemannian manifold. Here CLip...

Diffusion in an ultrametric space : a simple case