Higher order fluctuation fields and orthogonal duality polynomials

Mario Ayala; Gioia Carinci; Frank Redig

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arXiv · 2004.08412

Higher order fluctuation fields and orthogonal duality polynomials

Mario Ayala·Gioia Carinci·Frank Redig

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Abstract

Inspired by the works in [1] and [8] 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 discrete analogue of powers of the well-known density fluctuation field. We show that the weak limit of the $k$-th order field satisfies a recursive martingale problem that formally corresponds to the SPDE associated with the $k$th-power of a generalized Ornstein-Uhlenbeck process.

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Mario Ayala, Gioia Carinci, Frank Redig. 2020-04-17. Higher order fluctuation fields and orthogonal duality polynomials. https://arxiv.org/abs/2004.08412

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