Radoslaw Wojciechowski :
`Stochastic Incompleteness of the Heat Kernel on Graphs'

References for this talk:

1. Dodziuk, Joef; Mathai,Varghese :K`ato's inequality and asymptotic spectral properties for discrete magnetic Laplacians. The ubiquitous heat kernel, 69--81, Contemp. Math., 398, Amer. Math. Soc., Providence, RI, 2006.

2. Grigor'yan, Alexander: `Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds', Bull. Amer. Math. Soc. (N.S.) 36 (1999), no. 2, 135--249.

3. Wojciechowski, Radoslaw K., Heat kernel and essential spectrum of infinite graphs, Indiana Univ. Math. J. 58 No. 3 (2009), 1419-1442