Stochastic Duality and Eigenfunctions

Frank Redig, Federico Sau

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

1 Citation (Scopus)

Abstract

We start from the observation that, anytime two Markov generators share an eigenvalue, the function constructed from the product of the two eigenfunctions associated to this common eigenvalue is a duality function. We push further this observation and provide a full characterization of duality relations in terms of spectral decompositions of the generators for finite state space Markov processes. Moreover, we study and revisit some well-known instances of duality, such as Siegmund duality, and extract spectral information from it. Next, we use the same formalism to construct all duality functions for some solvable examples, i.e., processes for which the eigenfunctions of the generator are explicitly known.
Original languageEnglish
Title of host publicationStochastic Dynamics Out of Equilibrium - Institut Henri Poincaré, 2017
EditorsGiambattista Giacomin, Gabriel Stoltz, Herbert Spohn, Stefano Olla, Ellen Saada, Gabriel Stoltz
PublisherSpringer
Pages621-649
Number of pages29
Volume282
ISBN (Print)9783030150952
DOIs
Publication statusPublished - 2019
EventInternational workshop on Stochastic Dynamics out of Equilibrium, IHPStochDyn 2017 - Paris, France
Duration: 12 Jun 201716 Jun 2017

Publication series

NameProceedings in Mathematics & Statistics (PROMS)
PublisherSpringer
Volume282

Conference

ConferenceInternational workshop on Stochastic Dynamics out of Equilibrium, IHPStochDyn 2017
CountryFrance
CityParis
Period12/06/1716/06/17

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