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Ayala Valenzuela, M.A. (author), Carinci, G. (author), Redig, F.H.J. (author)Inspired by the works in [2] and [11] we introduce what we call k-th-order fluctuation fields and study their scaling limits. This construction is done in the context of particle systems with the property of orthogonal self-duality. This type of duality provides us with a setting in which we are able to interpret these fields as some type of...journal article 2021
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Groenevelt, W.G.M. (author), Giardina', C. (author), Redig, F.H.J. (author), Carinci, G. (author)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...journal article 2019
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Groenevelt, W.G.M. (author)We obtain stochastic duality functions for specific Markov processes using representation theory of Lie algebras. The duality functions come from the kernel of a unitary intertwiner between ∗-representations, which provides (generalized) orthogonality relations for the duality functions. In particular, we consider representations of the...journal article 2019
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Ayala Valenzuela, M.A. (author), Carinci, G. (author), Redig, F.H.J. (author)We study fluctuation fields of orthogonal polynomials in the context of particle systems with duality. We thereby obtain a systematic orthogonal decomposition of the fluctuation fields of local functions, where the order of every term can be quantified. This implies a quantitative generalization of the Boltzmann–Gibbs principle. In the...journal article 2018
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Redig, F.H.J. (author), Sau, F. (author)We find all self-duality functions of the form (Formula presented.)for a class of interacting particle systems. We call these duality functions of simple factorized form. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion processes, as well as...journal article 2018