Stochastically Incomplete Manifolds and Graphs

Details Stochastically Incomplete Manifolds and Graphs Stochastically Incomplete Manifolds and Graphs

2009-10-29

arxiv.org/abs/0910.5636v1

Physics

Mathematical Physics

17 pages

Scientific paper

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.

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