Volume growth and stochastic completeness of graphs

By M. Folz. 2012

98 citations recorded by the source corpus.

Given the variable-speed random walk on a weighted graph and a metric adapted to the structure of the random walk, we construct a Brownian motion on a closely related metric graph which behaves similarly to the VSRW and for which the associated intrinsic metric has certain desirable properties. Jump probabilities and moments of jump times for Brownian motion on metric graphs with varying edge lengths, jump conductances, and edge densities are computed. We use these results together with a theorem of Sturm for stochastic completeness, or non-explosiveness, on local Dirichlet spaces to prove sharp volume growth criteria in adapted metrics for stochastic completeness of graphs.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d5bccbabfb1fc814e22210a9e40101b831f3e54d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Radoslaw K. Wojciechowski
2. Matthias Keller
3. Frank Bauer
4. Lorenzo Rosasco

In Mathematical Physics

1. Matthias Keller
2. Radoslaw K. Wojciechowski
3. Frank Bauer
4. Daniel Lenz
5. Xueping Huang
6. Lorenzo Rosasco
7. J. Masamune
8. Sebastian Haeseler

In Statistics and Probability

1. Matthias Keller
2. Radoslaw K. Wojciechowski
3. Frank Bauer

Citations in the corpus

• Cheeger inequalities for unbounded graph Laplacians (2012, background): “[14, 15, 16, 23, 25, 30, 31, 32, 42], where certain variations of the concept also go under the name of adapted metrics.”