Related papers: A stochastic model of long-range interacting parti…
Macroscopic fluctuation theory has shown that a wide class of non-equilibrium stochastic dynamical systems obey a large deviation principle, but except for a few one-dimensional examples these large deviation principles are in general not…
We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilistic interpretation to obtain convergence towards equilibrium…
We investigate systems of self-propelled particles with alignment interaction. Compared to previous work, the force acting on the particles is not normalized and this modification gives rise to phase transitions from disordered states at…
Multi-phase phenomena remain at the heart of many challenging fluid dynamics problems. Molecular fluxes at the interface determine the fate of neighboring phases, yet their closure far from the continuum needs to be modeled. Along the…
We study a stochastic particle system with a logarithmically-singular inter-particle interaction potential which allows for inelastic particle collisions. We relate the squared Bessel process to the evolution of localized clusters of…
We study a general class of interacting particle systems over a countable state space $V$ where on each site $x \in V$ the particle mass $\eta(x) \geq 0$ follows a stochastic differential equation. We construct the corresponding Markovian…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…
The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton…
The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. In this paper, we derive a Fractional Fokker--Planck equation for the probability distribution of…
Certain types of active systems can be treated as an equilibrium system with excess non-conservative forces driving some of the microscopic degrees of freedom. We derive results for how many particles interacting with each other with both…
We discuss the dynamics and thermodynamics of systems with long-range interactions. We contrast the microcanonical description of an isolated Hamiltonian system to the canonical description of a stochastically forced Brownian system. We…
We study in this paper the longtime behavior of some large but finite populations of interacting stochastic differential equations whose (infinite population) limit Fokker-Planck PDE admits a stable periodic solution. We show that the…
The past two decades have seen a revolution in statistical physics, generalizing it to apply to systems of arbitrary size, evolving while arbitrarily far from equilibrium. Many of these new results are based on analyzing the dynamics of the…
We analyze energy spreading for a system that features mixed chaotic phase-space, whose control parameters (or slow degrees of freedom) vary quasi-statically. For demonstration purpose we consider the restricted 3~body problem, where the…
We investigate the bifurcation phenomena for stochastic systems with multiplicative Gaussian noise, by examining qualitative changes in mean phase portraits. Starting from the Fokker-Planck equation for the probability density function of…
We study a stochastic model of collective motion in which individuals update their orientation through pairwise aligning or anti-aligning copying interactions. We analyze both annealed dynamics, where interaction types are chosen…
The stochastic Kuramoto model defined on a sequence of graphs is analyzed: the emphasis is posed on the relationship between the mean field limit, the connectivity of the underlying graph and the long time behavior. We give an explicit…
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution…
We introduce a rejection-free continuous-time kinetic Monte Carlo framework to study stochastic systems governed by multiple concurrent dynamical mechanisms. In this approach, the relative activity of each dynamical channel emerges…
In this note we summarize the connections between equilibrium and slow out of equilibrium dynamics in finite dimensional glasses, such as we understand them today. If we assume that a finite-dimensional system is stable with respect to a…