Stochastic Completeness of Graphs
| dc.creator | Wojciechowski, Radoslaw K. | |
| dc.date | 2007-12-10 | |
| dc.date | 2007-12-11 | |
| dc.date.accessioned | 2026-07-07T08:48:22Z | |
| dc.date.available | 2026-07-07T08:48:22Z | |
| dc.description | In this thesis, we analyze the stochastic completeness of a heat kernel on graphs which is a function of three variables: a pair of vertices and a continuous time, for infinite, locally finite, connected graphs. For general graphs, a sufficient condition for stochastic completeness is given in terms of the maximum valence on spheres about a fixed vertex. That this result is optimal is shown by studying a particular family of trees. We also prove a lower bound on the bottom of the spectrum for the discrete Laplacian and use this lower bound to show that in certain cases the Laplacian has empty essential spectrum. | |
| dc.description | 72 pages, 1 figure, PhD thesis | |
| dc.identifier | https://arxiv.org/abs/0712.1570 | |
| dc.identifier | http://arxiv.org/abs/0712.1570 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143924 | |
| dc.subject | Spectral Theory | |
| dc.subject | Differential Geometry | |
| dc.title | Stochastic Completeness of Graphs | |
| dc.type | text |