相关论文: Scaling limits of Smoluchowski particles
Functional limit theorems for scaled fluctuations of occupation time processes of a sequence of critical branching particle systems in $\R^d$ with anisotropic space motions and strongly degenerated splitting abilities are proved in the…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
We have considered the underdamped motion of a Brownian particle in the presence of a correlated external random force. The force is modeled by an Ornstein-Uhlenbeck process. We investigate the fluctuations of the work done by the external…
We introduce a one-dimensional stochastic system where particles perform independent diffusions and interact through pairwise coagulation events, which occur at a nontrivial rate upon collision. Under appropriate conditions on the diffusion…
The distribution of a Markov process with killing, conditioned to be still alive at a given time, can be approximated by a Fleming-Viot type particle system. In such a system, each particle is simulated independently according to the law of…
We study a spatial Markovian particle system with pairwise coagulation, a spatial version of the Marcus--Lushnikov process: according to a coagulation kernel $K$, particle pairs merge into a single particle, and their masses are united. We…
We consider the small mass asymptotics (Smoluchowski-Kramers approximation) for the Langevin equation with a variable friction coefficient. The limit of the solution in the classical sense does not exist in this case. We study a…
We introduce a random matrix model for the stationary covariance of multivariate Ornstein-Uhlenbeck processes with heterogeneous temperatures, where the covariance is constrained by the Sylvester-Lyapunov equation. Using the replica method,…
Global solutions to the multicomponent Smoluchowski coagulation equation are constructed for measure-valued initial data with minimal assumptions on the moments. The framework is based on an abstract formulation of the Arzel\`a-Ascoli…
We study the Vlasov-Stokes equations which macroscopically model the sedimentation of a cloud of particles in a fluid, where particle inertia are taken into account but fluid inertia are assumed to be negligible. We consider the limit when…
This paper investigates a local central limit theorem for a normalized sequence of random variables belonging to a fixed order Wiener chaos and converging to the standard normal distribution. We prove, without imposing any additional…
We use the Chapman-Enskog method to derive the Smoluchowski equation from the Kramers equation in a high friction limit. We consider two main extensions of this problem: we take into account a uniform rotation of the background medium and…
We introduce an abstract Hilbert space-valued framework of Markovian lifts for stochastic Volterra equations with operator-valued Volterra kernels. Our main results address the existence and characterisation of possibly multiple limit…
In [20], the authors addressed the question of the averaging of a slow-fast Piecewise Deterministic Markov Process (PDMP) in infinite dimension. In the present paper, we carry on and complete this work by the mathematical analysis of the…
We analyze the dynamics of concentrated polymer solutions modeled by a 2D Smoluchowski equation. We describe the long time behavior of the polymer suspensions in a fluid. When the flow influence is neglected the equation has a gradient…
We prove the Central Limit Theorem for the number of eigenvalues near the spectrum edge for hermitian ensembles of random matrices. To derive our results, we use a general theorem, essentially due to Costin and Lebowitz, concerning the…
Let $\{Z_{m},m\geq 0\}$ be a critical branching process in random environment and $\{S_{m},m\geq 0\}$ be its associated random walk. Assuming that the increments distribution of the associated random walk belongs without centering to the…
The small mass limit is derived for a McKean-Vlasov equation subject to environmental noise with state-dependent friction. By applying the averaging approach to a non-autonomous stochastic slow-fast system with the microscopic and…
We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…
We rigorously derive non-equilibrium space-time fluctuation for the particle density of a system of reflected diffusions in bounded Lipschitz domains in $\mathbb R^d$. The particles are independent and are killed by a time-dependent…