English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper we prove a Feynman-Kac-It\^{o} formula for magneticSchr\"odinger operators on arbitrary weighted graphs. To do so, we have toprovide a natural and general framework both on the operator theoretic and theprobabilistic side of the equation. On the operator side we identify a verygeneral class of potentials that allows the definition of magneticSchr\"odinger operators. On the probabilistic side, we introduce an appropriatenotion of stochastic line integrals with respect to magnetic potentials. Apartfrom linking the world of discrete magnetic operators with the probabilisticworld through the Feynman-Kac-It\^{o} formula, the insights from this papergained on both sides should be of an independent interest. As applications ofthe Feynman-Kac-It\^{o} formula, we prove a Kato inequality, a Golden-Thompsoninequality and an explicit representation of the quadratic form domainscorresponding to a large class of potentials.

A Feynman-Kac-It\^o Formula for magnetic Schr\"odinger operators on graphs