We prove an a priori bound for the dynamic Φ^ 4_3 Φ 3 4 model on the torus which is
independent of the initial condition. In particular, this bound rules out the possibility of finite …

This note is an expanded version of a lecture I gave in fall 2021 at the MSRI program
“Universality and Integrability in Random Matrices and Interacting Particle Systems”. I will …

We review two works [Chandra et al., Publ. Math. l'IHÉS (published online, 2022) and
Chandra et al., arxiv: 2201.03487 (2022)] that study the stochastic quantization equations of …

We present a new construction of the Euclidean Φ^ 4 Φ 4 quantum field theory on R^ 3 R 3
based on PDE arguments. More precisely, we consider an approximation of the stochastic …

We define a state space and a Markov process associated to the stochastic quantisation
equation of Yang–Mills–Higgs (YMH) theories. The state space S is a nonlinear metric …

We provide a relatively compact proof of the BPHZ theorem for regularity structures of
decorated trees in the case where the driving noise satisfies a suitable spectral gap …

We define a natural state space and Markov process associated to the stochastic Yang–Mills
heat flow in two dimensions. To accomplish this we first introduce a space of distributional …

We prove that the stationary measures for the free-energy increment process for the
geometric last passage percolation (LPP) and log-gamma polymer model on a diagonal …

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 give a direct construction of invariant measures and global flows for the stochastic
quantization equation to the quantum field theoretical $\Phi^ 4_3 $-model on the $3 …