4 citations · 4 across the 1 of their papers we have counts for
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The parabolic Anderson model on a Galton-Watson tree
Frank den Hollander, Wolfgang König, Renato S. dos Santos
We study the long-time asymptotics of the total mass of the solution to the parabolic Anderson model (PAM) on a supercritical Galton-Watson random tree with bounded degrees. We ide…
Brownian motion in attenuated or renormalized inverse-square Poisson potential
Peter Nelson, Renato Soares dos Santos
We consider the parabolic Anderson problem with random potentials having inverse-square singularities around the points of a standard Poisson point process in , $d \g…
Random walk on random walks: low densities
Oriane Blondel, Marcelo R. Hilario, Renato Soares dos Santos +2
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of pertur…
Scaling of a random walk on a supercritical contact process
Frank den Hollander, Renato dos Santos
A proof is provided of a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The…