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Orthogonal Dualities of Markov Processes and Unitary Symmetries

Gioia Carinci, Technische Universiteit Delft, The Netherlands, Chiara Franceschini, Cristian Giardinà, Wolter Groenevelt, Frank Redig, Universidade de Lisboa, Portugal, University of Modena and Reggio Emilia, Italy, Technische Universiteit Delft, The Netherlands, Technische Universiteit Delft, The Netherlands
2019 Symmetry, Integrability and Geometry: Methods and Applications  

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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
more » ... ond 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.
doi:10.3842/sigma.2019.053 fatcat:6bjkfziyvrfd7dgtxzs245ajjm
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Gioia Carinci, Technische Universiteit Delft, The Netherlands, Chiara Franceschini, Cristian Giardinà, Wolter Groenevelt, Frank Redig, Universidade de Lisboa, Portugal, University of Modena and Reggio Emilia, Italy, Technische Universiteit Delft, The Netherlands, Technische Universiteit Delft, The Netherlands. "Orthogonal Dualities of Markov Processes and Unitary Symmetries." Symmetry, Integrability and Geometry: Methods and Applications (2019)