Brownian motion in attenuated or renormalized inverse-square Poisson potential

27 Jul 2020 Nelson Peter Santos Renato Soares dos

We consider the parabolic Anderson problem with random potentials having inverse-square singularities around the points of a standard Poisson point process in $\mathbb{R}^d$, $d \geq 3$. The potentials we consider are obtained via superposition of translations over the points of the Poisson point process of a kernel $\mathfrak{K}$ behaving as $\mathfrak{K}(x) \approx \theta |x|^{-2}$ near the origin, where $\theta \in (0,(d-2)^2/16]$... (read more)

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