The Feller Property for Graphs
Probability
2017-01-09 v2 Functional Analysis
Abstract
The Feller property concerns the preservation of the space of functions vanishing at infinity by the semigroup generated by an operator. We study this property in the case of the Laplacian on infinite graphs with arbitrary edge weights and vertex measures. In particular, we give conditions for the Feller property involving curvature-type quantities for general graphs, characterize the property in the case of model graphs, and give some comparison results to the model case.
Keywords
Cite
@article{arxiv.1411.0639,
title = {The Feller Property for Graphs},
author = {Radoslaw K. Wojciechowski},
journal= {arXiv preprint arXiv:1411.0639},
year = {2017}
}
Comments
17 pages. Shortened version with some typos corrected. Final version to appear in Transactions of the AMS