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.
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