5 papers
A spectral approach to the narrow escape problem in two-dimensional domains
Louis Carillo, Tony Lelièvre, Thomas Normand +1
We study the law of the exit time and exit point of a Brownian motion in a two-dimensional domain with reflecting boundary conditions, except on small disjoint exit windows through…
The narrow escape problem in arbitrary dimension
Louis Carillo, Tony Lelièvre, Thomas Normand +2
The narrow escape problem is a prototypical example for studying entropic metastability, motivated by the analysis of biological and chemical systems. The problem concerns the dete…
Spectral analysis of a semiclassical random walk associated to a general confining potential
Thomas Normand
We consider a semiclassical random walk with respect to a probability measure associated to a potential with a finite number of critical points. We recover the spectral results fro…
Spectral asymptotics and metastability for the linear relaxation Boltzmann equation
Thomas Normand
We consider the linear relaxation Boltzmann equation in a semiclassical framework. We construct a family of sharp quasimodes for the associated operator which yields sharp spectral…
Metastability results for a class of linear Boltzmann equations
Thomas Normand
We consider a semiclassical linear Boltzmann model with a non local collision operator. We provide sharp spectral asymptotics for the small spectrum in the low temperature regime f…