2 code implementations • 14 Jul 2019 • Tommaso Cornelis Rosati
We study the longtime behavior of KPZ-like equations: $$ \partial_{t}h(t, x) = \Delta_{x} h (t, x) + | \nabla_{x}h (t, x)|^{2} + \eta(t, x), \qquad h(0, x) = h_0(x), \qquad (t, x) \in (0, \infty) \times \mathbb{T}^{d} $$ on the $d-$dimensional torus $\mathbb{T}^{d}$ driven by an ergodic noise $\eta$ (e. g. space-time white in $d= 1$.
Probability 60H15, 37L55
no code implementations • 26 Jun 2019 • Tommaso Cornelis Rosati
This note extends the results in [8] to construct the rough super-Brownian motion on finite volume with Dirichlet boundary conditions.
Probability 60H15
no code implementations • 14 May 2019 • Nicolas Perkowski, Tommaso Cornelis Rosati
We study the scaling limit of a branching random walk in static random environment in dimension $d=1, 2$ and show that it is given by a super-Brownian motion in a white noise potential.
Probability 60H15, 35R60
