English

Simplicial branching random walks and their applications

Probability 2014-12-18 v1 Combinatorics Spectral Theory

Abstract

We define a new stochastic process on general simplicial complexes which allows to study their spectral and homological properties. Some results for random walks on graphs are shown to hold in this general setting. As an application, the process is used to calculate the spectral measure of high-dimensional analogues of regular trees and to construct solutions to the high-dimensional Dirichlet problem for forms.

Keywords

Cite

@article{arxiv.1412.5406,
  title  = {Simplicial branching random walks and their applications},
  author = {Ron Rosenthal},
  journal= {arXiv preprint arXiv:1412.5406},
  year   = {2014}
}

Comments

29 pages, 4 figures

R2 v1 2026-06-22T07:35:01.982Z