We consider the supercooled Stefan problem, which captures the freezing of a supercooled
liquid, in one space dimension. A probabilistic reformulation of the problem allows us to …

The present work concerns a version of the Fisher–KPP equation where the nonlinear term
is replaced by a saturation mechanism, yielding a free boundary problem with mixed …

Abstract The Branching Brownian Motion (BBM) process consists of particles performing
independent Brownian motions in\mathbb R, and each particle creating a new one at rate 1 …

We propose a deep learning strategy to estimate the mean curvature of two-dimensional
implicit interfaces in the level-set method. Our approach is based on fitting feed-forward …

We consider the facilitated exclusion process, which is a nonergodic, kinetically constrained
exclusion process. We show that in the hydrodynamic limit, its macroscopic behavior is …

We study a system of branching Brownian motions on R with annihilation: at each branching
time a new particle is created and the leftmost one is deleted. The case of strictly local …

We study a particle system without branching but with selection at timepoints depending on
a given probability distribution on the positive real line. The hydrodynamic limit of the particle …

We study large deviations for a Markov process on curves in ℤ 2 mimicking the motion of an
interface. Our dynamics can be tuned with a parameter β, which plays the role of an inverse …

The Bramson logarithmic shift of the position of pulled fronts is a universal feature common
to a large class of monostable traveling wave equations. As one varies the non-linearities it …

We propose a data-driven mean-curvature solver for the level-set method. This work is the
natural extension to R 3 of our two-dimensional error-correcting strategy presented in Larios …