Quantitative Boltzmann–Gibbs Principles via Orthogonal Polynomial Duality
Mario Ayala Valenzuela (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Gioia Carinci (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Frank Redig (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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Abstract
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 context of independent random walkers, we complete this program, including also fluctuation fields in non-stationary context (local equilibrium). For other interacting particle systems with duality such as the symmetric exclusion process, similar results can be obtained, under precise conditions on the n particle dynamics.
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