Orthogonal Dualities of Markov Processes and Unitary Symmetries

Symmetry Integrability and Geometry-Methods and Applications

article

Gioia Carinci¹  Chiara Franceschini²  Cristian Giardinà³  Wolter Groenevelt¹  Frank Redig¹ 

[1] Technische Universiteit Delft;Center for Mathematical Analysis Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa;University of Modena and Reggio Emilia

关键词: stochastic duality;    interacting particle systems;    Lie algebras;    orthogonal polynomial;   

DOI  :  10.3842/SIGMA.2019.053

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown