# Orthogonal Dualities of Markov Processes and Unitary Symmetries

@article{Carinci2019OrthogonalDO, title={Orthogonal Dualities of Markov Processes and Unitary Symmetries}, author={Gioia Carinci and Chiara Franceschini and Cristian Giardin{\`a} and Wolter G. M. Groenevelt and Frank Redig}, journal={Symmetry, Integrability and Geometry: Methods and Applications}, year={2019} }

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…

## 11 Citations

Stochastic Duality and Orthogonal Polynomials

- MathematicsSpringer Proceedings in Mathematics & Statistics
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For a series of Markov processes we prove stochastic duality relations with duality functions given by orthogonal polynomials. This means that expectations with respect to the original process (which…

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We study a class of interacting particle systems with asymmetric interaction showing a self-duality property. The class includes the ASEP(q, θ), asymmetric exclusion process, with a repulsive…

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In this paper we discuss a family of models of particle and energy diffusion on a one-dimensional lattice, related to those studied previously in [Sasamoto-Wadati], [Barraquand-Corwin] and…

Two Dualities: Markov and Schur–Weyl

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We show that quantum Schur-Weyl duality leads to Markov duality for a variety of asymmetric interacting particle systems. In particular, we consider three cases:
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We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the…

of the Bernoulli Society for Mathematical Statistics and Probability Volume Twenty Eight Number Two May 2022

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A list of forthcoming papers can be found online at http://www.bernoullisociety.org/index. php/publications/bernoulli-journal/bernoulli-journal-papers CONTENTS 713 BELLEC, P.C. and ZHANG, C.-H.…

Intertwining and Duality for Consistent Markov Processes

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In this paper we derive intertwining relations for a broad class of conservative particle systems both in discrete and continuous setting. Using the language of point process theory, we are able to…

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