Stochastic quantization associated with the exp⁡(Φ)2\exp(\Phi)_2-quantum field model driven by space-time white noise on the torus in the full L1L^1-regime

The present paper is a continuation of our previous work on the stochastic quantization of the $\exp(\Phi)_2$-quantum field model on the two-dimensional torus. Making use of key properties of Gaussian multiplicative chaos and refining the method for singular SPDEs introduced in the previous work, we construct a unique time-global solution to the corresponding parabolic stochastic quantization equation in the full "$L^{1}$-regime" $\vert\alpha\vert<\sqrt{8\pi}$ of the charge parameter $\alpha$. We also identify the solution with an infinite-dimensional diffusion process constructed by the Dirichlet form approach.Comment: References are correcte

A REGULARITY STRUCTURE FOR THE QUASILINEAR GENERALIZED KPZ EQUATION (Probability Symposium)

We prove the local well-posedness of a regularity structure formulation of the quasilinear generalized KPZ equation and give an explicit form for a renormalized equation in the full subcritical regime. This is an abstract of author's work [4]

Stochastic quantization associated with the exp(Φ)2exp(Φ)_2-quantum field model driven by space-time white noise on the torus

We consider a quantum field model with exponential interactions on the two-dimensional torus, which is called the $exp(Φ)_2$-quantum field model or Høegh-Krohn’s model. In the present paper, we study the stochastic quantization of this model by singular stochastic partial differential equations, which is recently developed. By the method, we construct a unique time-global solution and the invariant probability measure of the corresponding stochastic quantization equation and identify it with an infinite-dimensional diffusion process, which has been constructed by the Dirichlet form approach