We establish that global-in-time existence and non-uniqueness of probabilistically strong
solutions to the three dimensional Navier–Stokes system driven by space-time white noise …

We consider a natural class of ${\mathbf {R}}^ d $-valued one-dimensional stochastic partial
differential equations (PDEs) driven by space-time white noise that is formally invariant …

In this paper we study the large N limit of the O (N)-invariant linear sigma model, which is a
vector-valued generalization of the Φ 4 quantum field theory, on the three dimensional torus …

We develop a new stochastic analysis approach to the lattice Yang–Mills model at strong
coupling in any dimension d> 1, with t'Hooft scaling β N for the inverse coupling strength. We …

This paper is devoted to studying Hamilton-Jacobi-Bellman equations with distribution-
valued coefficients, which are not well-defined in the classical sense and are understood by …

Large N limit of the O(N) linear sigma model via stochastic quantization Page 1 The Annals of
Probability 2022, Vol. 50, No. 1, 131–202 https://doi.org/10.1214/21-AOP1531 © Institute of …

In this paper, we continue the study of large $ N $ problems for the Wick renormalized linear
sigma model, ie $ N $-component $\Phi^ 4$ model, in two spatial dimensions, using …

In this paper we introduce the stochastic Ricci flow (SRF) in two spatial dimensions. The flow
is symmetric with respect to a measure induced by Liouville conformal field theory. Using the …

In the paper, we construct conservative Markov processes corresponding to the martingale
solutions to the stochastic heat equation on $\mathbb {R}^+ $ or $\mathbb {R} $ with values …

We establish existence of an ergodic invariant measure on $ H^ 1 (D,\mathbb {R}^ 3)\cap L^
2 (D,\mathbb {S}^ 2) $ for the stochastic Landau-Lifschitz-Gilbert equation on a bounded one …