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2021 Higher order fluctuation fields and orthogonal duality polynomials
Mario Ayala, Gioia Carinci, Frank Redig
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Electron. J. Probab. 26: 1-35 (2021). DOI: 10.1214/21-EJP586


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 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 corresponds to the SPDE associated with the kth-power of a generalized Ornstein-Uhlenbeck process.

Funding Statement

M. Ayala acknowledges financial support from the Mexican Council on Science and Technology (CONACYT) via the scholarship 457347.


The authors would like to thank Federico Sau for helpful discussions; The authors also would like to thank valuable comments from anonymous reviewers.


Download Citation

Mario Ayala. Gioia Carinci. Frank Redig. "Higher order fluctuation fields and orthogonal duality polynomials." Electron. J. Probab. 26 1 - 35, 2021.


Received: 10 May 2020; Accepted: 30 January 2021; Published: 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.1214/21-EJP586

Primary: 35K55 , 60K35

Keywords: fluctuation fields , higher-order fields , orthogonal polynomials , self-duality


Vol.26 • 2021
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