198 research outputs found
Stochastic quantization associated with the -quantum field model driven by space-time white noise on the torus in the full -regime
The present paper is a continuation of our previous work on the stochastic
quantization of the -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 "-regime"
of the charge parameter . We also
identify the solution with an infinite-dimensional diffusion process
constructed by the Dirichlet form approach.Comment: References are correcte
Stochastic quantization associated with the exp-quantum field model and related topics (II) (Mathematical aspects of quantum fields and related topics)
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 -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 -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
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