Orthogonal dualities of Markov processes and unitary symmetries
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Publication:2330824
DOI10.3842/SIGMA.2019.053zbMATH Open1423.60116arXiv1812.08553MaRDI QIDQ2330824
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Publication date: 23 October 2019
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1812.08553
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