Related papers: Interacting particle systems with continuous spins
In this paper, we study the estimation of drift and diffusion coefficients in a two dimensional system of N interacting particles modeled by a degenerate stochastic differential equation. We consider both complete and partial observation…
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…
We study the dynamics of an infinite system of point particles of two types. They perform random jumps in $\mathbf{R}^d$ in the course of which particles of different types repel each other whereas those of the same type do not interact.…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
A new particle-based sampling and approximate inference method, based on electrostatics and Newton mechanics principles, is introduced with theoretical ground, algorithm design and experimental validation. This method simulates an…
We construct a family of semimartingales that describes the behavior of a particle system with sticky-reflecting interaction. The model is a physical improvement of the Howitt-Warren flow, an infinite system of diffusion particles on the…
We study a system of reflected Brownian motions on the positive half-line in which each particle has a drift toward the origin determined by the local times at the origin of all the particles. If this local time drift is too strong, such…
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…
Dynamical systems of N particles in \R^{D} interacting by a singular pair potential of mean field type are considered. The systems are assumed to be of gradient type and the existence of a macroscopic limit in the many particle limit is…
In this paper, we derive fully implementable first order time-stepping schemes for McKean--Vlasov stochastic differential equations (McKean--Vlasov SDEs), allowing for a drift term with super-linear growth in the state component. We propose…
In this article, we study an interacting particle system in the context of epidemiology where the individuals (particles) are characterized by their position and infection state. We begin with a description at the microscopic level where…
We consider a discrete particle system of two species coupled through nonlocal interactions driven by the one-dimensional Newtonian potential, with repulsive self-interaction and attractive cross-interaction. After providing a suitable…
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
The s=1/2 Ising chain with uniform nearest-neighbor and next-nearest-neighbor coupling is used to construct a system of floating particles characterized by motifs of up to six consecutive local spins. The spin couplings cause the assembly…
We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction…
\noindent Consider an infinite collection of particles on the real line moving according to independent Brownian motions and such that the $i$-th particle from the left gets the drift $g_{i-1}$. The case where $g_0=1$ and $g_{i}=0$ for all…
We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P_0(v), while the slow particle remains…
We consider a general system of n noninteracting identical particles which evolve under a given dynamical law and whose initial microstates are a priori independent. The time evolution of the n-particle average of a bounded function on the…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
We obtain the hydrodynamic limit of one-dimensional interacting particle systems describing the macroscopic evolution of the density of mass in infinite volume from the microscopic dynamics. The processes are weak pertubations of the…