English

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

R2 v1 2026-06-21T14:04:54.012Z