Work

Non-Gaussianity of invariant measures to SPDEs in Da Prato–Debussche regime

Year: 2025

Type: article

Abstract: We propose an elementary method to show non-Gaussianity of invariant measures of parabolic stochastic partial differential equations with polynomial non-linearities in the Da Prato–Debussche regime. The approach is essentially algebraic and involves using the generator equation of the SPDE at stationarity. Our results in particular cover the $$\Phi ^4_\delta $$ Φ δ 4 measures in dimensions $$\delta <\frac{14}{5}$$ δ < 14 5 , which includes cases where the invariant measure is singular with respect to the invariant measure of the linear solution.

Source: Stochastic Partial Differential Equations Analysis and Computations

DOI: 10.1007/s40072-025-00370-3

Authors: Ajay Chandra, Ilya Chevyrev

Institutions: Imperial College London, Scuola Internazionale Superiore di Studi Avanzati

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Deutsche Forschungsgemeinschaft, Technische Universität Berlin, Engineering and Physical Sciences Research Council