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 -