Decay of harmonic functions for discrete time Feynman–Kac operators with confining potentials
Publikation: Beitrag in Fachzeitschrift › Forschungsartikel › Beigetragen › Begutachtung
Beitragende
Abstract
We propose and study a certain discrete time counterpart of the classical Feynman–Kac semigroup with a confining potential in a countably infinite space. For a class of long range Markov chains which satisfy the direct step property we prove sharp estimates for functions which are (sub-, super-)harmonic in infinite sets with respect to the discrete Feynman–Kac operators. These results are compared with respective estimates for the case of a nearest-neighbour random walk which evolves on a graph of finite geometry. We also discuss applications to the decay rates of solutions to equations involving graph Laplacians and to eigenfunctions of the discrete Feynman–Kac operators. We include such examples as non-local discrete Schrödinger operators based on fractional powers of the nearest-neighbour Laplacians and related quasi-relativistic operators. Finally, we analyse various classes of Markov chains which enjoy the direct step property and illustrate the obtained results by examples.
Details
Originalsprache | Englisch |
---|---|
Seiten (von - bis) | 1071-1101 |
Seitenumfang | 31 |
Fachzeitschrift | Alea (Rio de Janeiro) |
Jahrgang | 19 |
Ausgabenummer | 1 |
Publikationsstatus | Veröffentlicht - 2022 |
Peer-Review-Status | Ja |
Schlagworte
ASJC Scopus Sachgebiete
Schlagwörter
- Direct step property, Eigenfunction, Feynman-kac formula, Ground state, Markov chain, Schrödinger semigroup, Weighted graph