Abstract: In this third talk of the lecture series, I will consider the three-dimensional case. I will first discuss the construction of the $\Phi^3_3$-measure with a cubic interaction potential. This problem turns out to be critical, exhibiting a phase transition: normalizability in the weakly nonlinear regime and non-normalizability in the strongly nonlinear regime. Then, I will discuss the dynamical problem for the canonical stochastic quantization of the $\Phi^3_3$-measure, namely, the three-dimensional stochastic damped nonlinear wave equation with a quadratic nonlinearity forced by an additive space-time white noise (= the hyperbolic $\Phi^3_3$-model). As for the local theory, I will describe the paracontrolled approach to study stochastic nonlinear wave equations, introduced in my work with Gubinelli and Koch (2018). In the globalization part, I introduce a new, conceptually simple and straightforward approach, where we directly work with the (truncated) Gibbs measure, using the variational formula and ideas from theory of optimal transport. This third talk is based on a joint work with Mamoru Okamoto (Osaka), and Leonardo Tolomeo (Bonn).
Zoom Information
https://zoom.us/j/85264608233?pwd=Ti8xR2ZORHdzY25YbG1TV2p2N29ydz09
Conference Number：852 6460 8233
Password：825932
