Abstract:
We restrict the $\Phi^4$ dynamics on a 2D surface embedded in a 3D torus, with an effective fractional dimension $d\in(2,4)$. We prove that when $d\in(2,3)$, the solution at a fixed time is mutually absolutely continuous with respect to the corresponding linear solution. To circumvent the irregularity of the nonlinearity, we construct an auxiliary process that coincides with $\Phi^4$ dynamics on the surface at a fixed time, but is driven by a modified drift of sufficient regularity and integrability. This talk is based on the joint work with Martin Hairer.
Biography:
Fanhao Kong is a fifth-year PhD student at Peking University. His research focuses on stochastic analysis and stochastic partial differential equation.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.