Quantitative Boltzmann Gibbs principles via orthogonal polynomial duality

Mario Ayala; Gioia Carinci; Frank Redig

doi:10.1007/s10955-018-2060-7

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arXiv · 1712.08492

Quantitative Boltzmann Gibbs principles via orthogonal polynomial duality

Mario Ayala·Gioia Carinci·Frank Redig

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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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Mario Ayala, Gioia Carinci, Frank Redig. 2017-12-22. Quantitative Boltzmann Gibbs principles via orthogonal polynomial duality. https://doi.org/10.1007/s10955-018-2060-7

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