Related papers: Self-interacting diffusions IV: Rate of convergenc…
Reflected diffusions naturally arise in many problems from applications ranging from economics and mathematical biology to queueing theory. In this paper we consider a class of infinite time-horizon singular stochastic control problems for…
We introduce an interacting particle system that models the spread of an epidemic in terms of heterogeneous diffusive dynamics, rather than exogenous contact and transmission rates at the population level as in classical compartmental…
Reaction-diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem.…
Reversible diffusion limited cluster aggregation of hard spheres with rigid bonds was simulated and the self diffusion coefficient was determined for equilibrated systems. The effect of increasing attraction strength was determined for…
We report a new phenomenon, called self-recovery, in the process of diffusion in a region with boundary. Suppose that a diffusing quantity is uniformly distributed initially and then gets excited by the change in the boundary values over a…
Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the…
Four results associated with the diffuse-interface model (DIM) for contact lines are reported in this paper. First, a boundary condition is derived, which states that the fluid near a solid wall must have a certain density $\rho_{0}$…
This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…
Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are…
In this paper, we consider the problem of joint parameter estimation for drift and diffusion coefficients of a stochastic McKean-Vlasov equation and for the associated system of interacting particles. The analysis is provided in a general…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
We consider a reaction-diffusion process with retardation. The particles, immersed in traps initially, remain inactive until another particle is annihilated spontaneously with a rate $\lambda$ at a certain point $\vec x$. In that case the…
We study a two-component reaction-diffusion system in which one of the reaction terms becomes singularly large. Assuming that the initial data are nonnegative and mutually segregated, we prove that the solution converges to that of the heat…
The dark matter density distribution in small-scale astrophysical objects may indicate that dark matter is self-interacting, while observations from clusters of galaxies suggest that the corresponding cross section depends on the velocity.…
The Einstein relation describes the response of a diffusing particle to a small constant external force. It states that, as the force tends to zero, the ratio of the limiting velocity to the force magnitude converges to the diffusivity…
Stochastic interactions generically enhance self-diffusivity in living and biological systems, e.g. optimizing navigation strategies and controlling material properties of cellular tissues and bacterial aggregates. Despite this, the…
We consider a sequence of systems of Hawkes processes having mean field interactions in a diffusive regime. The stochastic intensity of each process is a solution of a stochastic differential equation driven by N independent Poisson random…
A self-interacting velocity jump process is introduced, which behaves in large time similarly to the corresponding self-interacting diffusion, namely the evolution of its normalized occupation measure approaches a deterministic flow.
The behavior of the self diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare…
This paper studies the asymptotic behavior of processes with switching. More precisely, the stability under fast switching for diffusion processes and discrete state space Markovian processes is considered. The proofs are based on…