We show that the Markov semigroups generated by a large class of singular stochastic
PDEs satisfy the strong Feller property. These include for example the KPZ equation and the …

We study the long time behavior of the stochastic quantization equation. Extending recent
results by Mourrat and Weber (Global well-posedness of the dynamic ϕ^4 in the plane …

We study Gibbs measures with log-correlated base Gaussian fields on the $ d $-
dimensional torus. In the defocusing case, the construction of such Gibbs measures follows …

We consider a quantum field model with exponential interactions on the two-dimensional
torus, which is called the\exp (Φ) _ 2 exp (Φ) 2-quantum field model or Høegh-Krohn's …

We provide a rigorous derivation of nonlinear Gibbs measures in two and three space
dimensions, starting from many-body quantum systems in thermal equilibrium. More …

We consider the stochastic Yang-Mills heat equation on the two-dimensional torus. Using
regularity structures, Chandra, Chevyrev, Hairer, and Shen previously proved both the local …

We prove that Gibbs measures based on 1D defocusing nonlinear Schrödinger functionals
with sub-harmonic trapping can be obtained as the mean-field/large temperature limit of the …

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 …

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 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 …