Stochastically Incomplete Manifolds and Graphs
Mathematical Physics
2009-10-30 v1 math.MP
Abstract
We survey geometric properties which imply the stochastic incompleteness of the minimal diffusion process associated to the Laplacian on manifolds and graphs. In particular, we completely characterize stochastic incompleteness for spherically symmetric graphs and show that, in contrast to the case of Riemannian manifolds, there exist examples of stochastically incomplete graphs of polynomial volume growth.
Cite
@article{arxiv.0910.5636,
title = {Stochastically Incomplete Manifolds and Graphs},
author = {Radoslaw Krzysztof Wojciechowski},
journal= {arXiv preprint arXiv:0910.5636},
year = {2009}
}
Comments
17 pages