TY - GEN

T1 - Stochastic Duality and Eigenfunctions

AU - Redig, Frank

AU - Sau, Federico

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85069483551&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-15096-9_25

DO - 10.1007/978-3-030-15096-9_25

M3 - Conference contribution

AN - SCOPUS:85069483551

SN - 9783030150952

VL - 282

T3 - Proceedings in Mathematics & Statistics (PROMS)

SP - 621

EP - 649

BT - Stochastic Dynamics Out of Equilibrium - Institut Henri Poincaré, 2017

A2 - Giacomin, Giambattista

A2 - Stoltz, Gabriel

A2 - Spohn, Herbert

A2 - Olla, Stefano

A2 - Saada, Ellen

A2 - Stoltz, Gabriel

PB - Springer

T2 - International workshop on Stochastic Dynamics out of Equilibrium, IHPStochDyn 2017

Y2 - 12 June 2017 through 16 June 2017

ER -