We consider the parabolic stochastic quantization equation associated to the $\Phi^4_2$ model on the torus in a spatial white noise environment. We study the long time behavior of this heat equation with independent multiplicative white noise and additive spacetime white noise and prove convergence towards a unique invariant measure.
May, 2025
We study a counterpart to the quasilinear generalized parabolic Anderson model on the 2-dimensional torus where the coefficients are nonlocal functionals of the solution.
May, 2024
We study a counterpart to the quasilinear generalized parabolic Anderson model on the 2-dimensional torus where the coefficients are nonlocal functionals of the solution.
May, 2024
We study the parabolic defocusing stochastic quantization equation with both mutliplicative spatial white noise and an independant space-time white noise forcing, on compact surfaces, with polynomial nonlinearity.
Jan, 2024
We study the parabolic defocusing stochastic quantization equation with both mutliplicative spatial white noise and an independant space-time white noise forcing, on compact surfaces, with polynomial nonlinearity.
Jan, 2024
We use some tools from nonlinear analysis to study two examples of singular stochastic elliptic PDEs that cannot be solved by the contraction principle or the Schauder fixed point theorem.
Feb, 2022
We use some tools from nonlinear analysis to study two examples of singular stochastic elliptic PDEs that cannot be solved by the contraction principle or the Schauder fixed point theorem.
Feb, 2022