A simple construction of the continuum parabolic Anderson model on ${\mathbf{R}}^2$

Abstract

We propose a simple construction of the solution to the continuum parabolic Anderson model on ${\mathbf{R}}^2$ which does not rely on any elaborate arguments and makes extensive use of the linearity of the equation. A logarithmic renormalisation is required to counterbalance the divergent product appearing in the equation. Furthermore, we use time-dependent weights in our spaces of distributions in order to construct the solution on the unbounded space ${\mathbf{R}}^2$.

References in corpus (1)

• A simple construction of the continuum parabolic Anderson model on ${\mathbf{R}}^2$

Cited by in corpus (29)

• A simple construction of the continuum parabolic Anderson model on ${\mathbf{R}}^2$
• Global solutions to elliptic and parabolic ${\Phi }^4$ models in Euclidean space
• Multidimensional SDE with distributional drift and Lévy noise
• Stationary solutions to the stochastic Burgers equation on the line
• Algebraic renormalisation of regularity structures
• KPZ equation limit of sticky Brownian motion
• Modulation Equation for SPDEs in unbounded domains with space-time white noise -- Linear Theory
• Integrated density of states of the Anderson Hamiltonian with two-dimensional white noise
• An introduction to singular stochastic PDEs: Allen-Cahn equations, metastability and regularity structures
• Local and global well-posedness of 2d periodic multiplicative stochastic NLS
• Boundary renormalisation of SPDEs
• The weak coupling limit for the random Schrödinger equation: The average wave function
• Stochastic parabolic equations with singular potentials
• Longtime asymptotics of the two-dimensional parabolic Anderson model with white-noise potential
• The stochastic heat equation with multiplicative Lévy noise: Existence, moments, and intermittency
• Multiplicative SHE limit of random walks in space-time random environments
• A stochastic sewing lemma and applications
• Heat semigroup and singular PDEs
• KPZ fluctuations in the planar stochastic heat equation
• Phase Transitions in Asymptotically Singular Anderson Hamiltonian and Parabolic Model
• A simple construction of the dynamical ${\Phi }_3^4$ model
• Scaling limit of a directed polymer among a Poisson field of independent walks
• Singular SPDEs on Homogeneous Lie Groups
• Global well-posedness for the nonlinear generalized parabolic Anderson model equation
• The continuum parabolic Anderson model with a half-Laplacian and periodic noise
• Construction and spectrum of the Anderson Hamiltonian with white noise potential on ${\mathbf{R}}^2$ and ${\mathbf{R}}^3$
• Moments of 2D Parabolic Anderson Model
• Constraint Minimization Problem of the Nonlinear Schrödinger Equation with the Anderson Hamiltonian
• Anderson Hamiltonians with singular potentials