4 papers · 1 filter
Exponential mixing for random dynamical systems and an example of Pierrehumbert
Alex Blumenthal, Michele Coti Zelati, Rishabh S. Gvalani
We consider the question of exponential mixing for random dynamical systems on arbitrary compact manifolds without boundary. We put forward a robust, dynamics-based framework that…
Phase transitions for nonlinear nonlocal aggregation-diffusion equations
José A. Carrillo, Rishabh S. Gvalani
We are interested in studying the stationary solutions and phase transitions of aggregation equations with degenerate diffusion of porous medium-type, with exponent $1 < m < \infty…
Barriers of the McKean--Vlasov energy via a mountain pass theorem in the space of probability measures
Rishabh S. Gvalani, André Schlichting
We show that the empirical process associated with a system of weakly interacting diffusion processes exhibits a form of noise-induced metastability. The result is based on an anal…
Long-time behaviour and phase transitions for the McKean--Vlasov equation on the torus
J. A. Carrillo, R. S. Gvalani, G. A. Pavliotis +1
We study the McKean-Vlasov equation \[ \partial_t \varrho= β^{-1} Δ\varrho + κ\nabla \cdot (\varrho \nabla (W \star \varrho)) \, , \] with periodic boundary conditions on the torus…