Anderson stochastic quantization equation

Hugo Eulry (1) , Antoine Mouzard (2) , Tristan Robert (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 DMA - Département de Mathématiques et Applications - ENS Paris
3 IECL - Institut Élie Cartan de Lorraine

We study the parabolic defocusing stochastic quantization equation with both mutliplicative spatial white noise and an independant space-time white noise forcing, on compact surfaces, with polynomial nonlinearity. After renormalizing the nonlinearity, we construct the random Gibbs measure as an absolutely continuous measure with respect to the law of the Anderson Gaussian Free Field for fixed realization of the spatial white noise. Then, when the initial data is distributed according to the Gibbs measure, we prove almost sure global well-posedness for the dynamics and invariance of the Gibbs measure.

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Hugo Eulry, Antoine Mouzard, Tristan Robert. Anderson stochastic quantization equation. 2024. ⟨hal-04413765⟩