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Mathematics > Probability

arXiv:1812.08553 (math)
[Submitted on 20 Dec 2018 (v1), last revised 12 Jul 2019 (this version, v3)]

Title:Orthogonal Dualities of Markov Processes and Unitary Symmetries

Authors:Gioia Carinci, Chiara Franceschini, Cristian Giardinà, Wolter Groenevelt, Frank Redig
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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.
Subjects: Probability (math.PR); Mathematical Physics (math-ph); Classical Analysis and ODEs (math.CA)
Cite as: arXiv:1812.08553 [math.PR]
  (or arXiv:1812.08553v3 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1812.08553
Journal reference: SIGMA 15 (2019), 053, 27 pages
Related DOI: https://doi.org/10.3842/SIGMA.2019.053

Submission history

From: Chiara Franceschini [view email] [via SIGMA proxy]
[v1] Thu, 20 Dec 2018 13:38:01 UTC (34 KB)
[v2] Wed, 24 Apr 2019 15:29:15 UTC (36 KB)
[v3] Fri, 12 Jul 2019 05:12:01 UTC (27 KB)
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