We investigate the infinite volume limit of the variational description of Euclidean quantum
fields introduced in a previous work. Focusing on two-dimensional theories for simplicity, we …

The (elliptic) stochastic quantization equation for the (massive) $\cosh (\beta\varphi) _2 $
model, for the charged parameter in the $ L^ 2$ regime (ie $\beta^ 2< 4\pi $), is studied. We …

Building on previous work on the stochastic analysis for Grassmann random variables, we
introduce a forward-backward stochastic differential equation (FBSDE) which provides a …

We introduce a stochastic analysis of Grassmann random variables suitable for the
stochastic quantization of Euclidean fermionic quantum field theories. Analysis on …

The $\Phi^ 4_3 $ measure is one of the easiest non-trivial examples of a Euclidean quantum
field theory (EQFT) whose rigorous construction in the 1970's has been one of the …

We derive a priori bounds for the Φ 4 equation in the full sub-critical regime using Hairer's
theory of regularity structures. The equation is formally given by where the term+∞ ϕ …

The present paper is a continuation of our previous work (Hoshino et al., J Evol Equ 21: 339–
375, 2021) on the stochastic quantization of the exp (Φ) 2-quantum field model on the two …

We present two approaches to establish the exponential decay of correlation functions of
Euclidean quantum field theories (EQFTs) via stochastic quantization (SQ). In particular we …

We consider space-time quantum fields with exponential/trigonometric interactions. In the
context of Euclidean quantum field theory, the former and the latter are called the Høegh …

We prove that there exists a diffusion process whose invariant measure is the three
dimensional polymer measure $\nu_\lambda $ for small $\lambda> 0$. We follow in part a …