As a counterpoint to classical stochastic particle methods for diffusion, we develop a
deterministic particle method for linear and nonlinear diffusion. At first glance, deterministic …

Inferring the laws of interaction in agent-based systems from observational data is a
fundamental challenge in a wide variety of disciplines. We propose a nonparametric …

The aim of this survey is to serve as an introduction to the different techniques available in
the broad field of aggregation-diffusion equations. We aim to provide historical context, key …

The repulsion strength at the origin for repulsive/attractive potentials determines the
regularity of local minimizers of the interaction energy. In this paper, we show that if this …

The existence of compactly supported global minimisers for continuum models of particles
interacting through a potential is shown under almost optimal hypotheses. The main …

For the interaction energy with repulsive–attractive potentials, we give generic conditions
which guarantee the radial symmetry of the local minimizers in the infinite Wasserstein …

We consider a family of interaction functionals consisting of power-law potentials with
attractive and repulsive parts and use the concentration compactness principle to establish …

We show that the support of any local minimizer of the interaction energy consists of isolated
points whenever the interaction potential is of class C2 and mildly repulsive at the origin; …

We consider a class of nonlocal shape optimization problems for sets of fixed mass where
the energy functional is given by an attractive/repulsive interaction potential in powerlaw …

We solve explicitly a certain minimization problem for probability measures in one
dimension involving an interaction energy that arises in the modeling of aggregation …