Stochastically Incomplete Manifolds and Graphs

Conference paper

DOI: 10.1007/978-3-0346-0244-0_9

Part of the Progress in Probability book series (PRPR, volume 64)
Cite this paper as:
Wojciechowski R.K. (2011) Stochastically Incomplete Manifolds and Graphs. In: Lenz D., Sobieczky F., Woess W. (eds) Random Walks, Boundaries and Spectra. Progress in Probability, vol 64. Springer, Basel

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.

Keywords

Stochastic incompleteness explosion heat kernel manifolds graphs curvature volume growth 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Grupo de Física-MatemáticaComplexo Interdisciplinar da Universidade de LisboaLisboaPortugal

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