01/03/2023, 16:00 — 17:00 — Online
Mario Ayala, Technische Universität München
Fluctuation fields and orthogonal self-dualities
In the study of scaling limits of reversible particle systems with the property of self-duality, many quantities of interest become easier to manipulate and simplify. For the particular case of fluctuations from the hydrodynamic limit, and in the additional presence of orthogonality, these simplifications have interesting consequences. In this talk, we will briefly discuss some of those consequences. First, we will 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. Second we will introduce what we call the k-th order fluctuation field. We will then explain how these fields can be interpreted as some type of discrete analogue of powers of the well-known density fluctuation field, and show how their scaling limits formally correspond to the SPDE associated with the kth-power of a generalized Ornstein-Uhlenbeck process.
This work takes inspiration from [1] and [2], and it is a joint effort with G. Carinci (Università di Modena e R. Emilia) and Frank Redig (TU Delft).
- Sigurd Assing, A limit theorem for quadratic fluctuations in symmetric simple exclusion, Stochastic Process. Appl. 117 (2007), no. 6, 766–790.
- Patrícia Gonçalves and Milton Jara, Quadratic fluctuations of the symmetric simple exclusion, ALEA Lat. Am. J. Probab. Math. Stat. 16 (2019), no. 1, 605–632.
