We review a class of gradient systems with dissipation potentials of hyperbolic-cosine type.
We show how such dissipation potentials emerge in large deviations of jump processes …

We study a class of nonlocal partial differential equations presenting a tensor-mobility, in
space, obtained asymptotically from nonlocal dynamics on localising infinite graphs. Our …

We consider the Wasserstein metric on the Gaussian mixture models (GMMs), which is
defined as the pullback of the full Wasserstein metric on the space of smooth probability …

We consider finite-volume approximations of Fokker--Planck equations on bounded convex
domains in R^d and study the corresponding gradient flow structures. We reprove the …

We introduce a family of various finite volume discretization schemes for the Fokker–Planck
operator, which are characterized by different Stolarsky weight functions on the edges. This …

This paper deals with the large-scale behaviour of dynamical optimal transport on Z d-
periodic graphs with general lower semicontinuous and convex energy densities. Our main …

Motivated by applications in data science, we study partial differential equations on graphs.
By a classical fixed-point argument, we show existence and uniqueness of solutions to a …

We perform a fast-reaction limit for a linear reaction-diffusion system consisting of two
diffusion equations coupled by a linear reaction. We understand the linear reaction-diffusion …

We provide a well-posedness theory for a class of nonlocal continuity equations on co-
evolving graphs. We describe the connection among vertices through an edge weight …

We consider three classical models of biological evolution:(i) the Moran process, an
example of a reducible Markov Chain;(ii) the Kimura Equation, a particular case of a …