Inspired by the works in  and  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.
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.
"Higher order fluctuation fields and orthogonal duality polynomials." Electron. J. Probab. 26 1 - 35, 2021. https://doi.org/10.1214/21-EJP586