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 …

In this paper we mainly investigate the strong and weak well-posedness of a class of
McKean–Vlasov stochastic (partial) differential equations. The main existence and …

In this Review, we review some recent rigorous results on large N problems in quantum field
theory, stochastic quantization, and singular stochastic partial differential equations (SPDEs) …

In this paper we explore the merit of relative entropy in proving weak well-posedness of
McKean-Vlasov SDEs and SPDEs, extending the technique introduced in Lacker arxiv …

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 …

In this paper, we provide a general framework for investigating McKean-Vlasov stochastic
partial differential equations. We first show the existence of weak solutions by combining the …

Quantitative estimates for the top Lyapunov exponents for systems of stochastic reaction-
diffusion equations are proven. The treatment includes reaction potentials with degenerate …

This work considers the two-dimensional Allen–Cahn equation∂ tu= 1 2 Δ u+ mu-u 3, u (0,
x)= η (x),∀(t, x)∈[0,∞)× R 2, where the initial condition η is a two-dimensional white noise …

We study asymptotic expansions of the Euclidean $\Phi^ 4_2 $-measure in the low-
temperature regime. In particular, this extends the asymptotic expansions of Gaussian …

In this paper we study the perturbation theory of $\Phi^ 4_2 $ model on the whole plane via
stochastic quantization. We use integration by parts formula (ie Dyson-Schwinger equations) …