Orthogonal Dualities of Markov Processes and Unitary Symmetries

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.

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Cited by in corpus (10)

• A reverse duality for the ASEP with open boundaries
• Symmetric inclusion process with slow boundary: hydrodynamics and hydrostatics
• Integrable heat conduction model
• Markov duality and Bethe ansatz formula for half-line open ASEP
• Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations
• Orthogonal Polynomial Stochastic Duality Functions for Multi-Species SEP$(2j)$ and Multi-Species IRW
• Orthogonal polynomial duality of a two-species asymmetric exclusion process
• Orthogonal Intertwiners for Infinite Particle Systems in The Continuum
• A Generalized Dynamic Asymmetric Exclusion Process: Orthogonal Dualities and Degenerations
• Intertwinings for Continuum Particle Systems: an Algebraic Approach