Orthogonal Dualities of Markov Processes and Unitary Symmetries

Groenevelt, W.G.M.; Giardina', C.; Redig, F.H.J.; Carinci, G.

doi:10.3842/SIGMA.2019.053

Orthogonal Dualities of Markov Processes and Unitary Symmetries

Title

Orthogonal Dualities of Markov Processes and Unitary Symmetries

Author

Groenevelt, W.G.M. (TU Delft Analysis)
Giardina', C. (TU Delft Applied Probability)
Redig, F.H.J. (TU Delft Applied Probability)
Carinci, G. (TU Delft Applied Probability)

Date

2019-07-12

Abstract

We study self-duality for interacting particle systems, where the particles move as continuous time random walkers having either exclusion interaction or inclusion interaction. We show that orthogonal self-dualities arise from unitary symmetries of the Markov generator. For these symmetries we provide two equivalent expressions that are related by the Baker-Campbell-Hausdorff formula. The first expression is the exponential of an anti Hermitian operator and thus is unitary by inspection; the second expression is factorized into three terms and is proved to be unitary by using generating functions. The factorized form is also obtained by using an independent approach based on scalar products, which is a new method of independent interest that we introduce to derive (bi)orthogonal duality functions from non-orthogonal duality functions.

Subject

Interacting particle systems
Lie algebras
Orthogonal polynomials
Stochastic duality

To reference this document use:

http://resolver.tudelft.nl/uuid:49302195-d43c-45d8-8a8e-afe3ce0352fa

DOI

https://doi.org/10.3842/SIGMA.2019.053

ISSN

1815-0659

Source

Symmetry, Integrability and Geometry: Methods and Applications, 15 (53)

Part of collection

Institutional Repository