相关论文: Transience of second-class particles and diffusive…

We show that the distribution of times for a diffusing particle to first hit an absorber is \emph{independent} of the direction of an external flow field, when we condition on the event that the particle reaches the target for flow away…

We investigate the escape behavior of systems governed by the one-dimensional nonlinear diffusion equation $\partial_t \rho = \partial_x[\partial_x U\rho] + D\partial^2_x \rho^\nu$, where the potential of the drift, $U(x)$, presents a…

We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ${\Bbb R}^d$ or ${\Bbb Z}^d$. The first class consists of random walks on ${\Bbb Z}^d$ in divergence-free random drift field,…

Local perturbations in conservative particle systems can have a non-local influence on the stationary measure. To capture this phenomenon, we analyze in this paper two toy models. We study the symmetric exclusion process on a countable set…

Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…

Consider a system of particles performing nearest neighbor random walks on the lattice $\ZZ$ under hard--core interaction. The rate for a jump over a given bond is direction--independent and the inverse of the jump rates are i.i.d. random…

In one and two dimensions, the first-passage time for a diffusing particle in the presence of a radial potential flow to hit a sphere, conditioned on actually hitting the sphere, is independent of the sign of the drift. Moreover, the…

Consider a discrete time Markov process $X^\epsilon$ on $\mathbf R^d$ that makes a deterministic jump based on its current location, and then takes a small Gaussian step of variance $\epsilon^2$. We study the behavior of the asymptotic…

We discuss a family of time-inhomogeneous two-dimensional diffusions, defined over a finite time interval $[0,T]$, having transition density functions that are expressible in terms of the integral kernels for negative exponentials of the…

We propose a unifying theoretical framework for the analysis of first-passage time distributions in two important classes of stochastic processes in which the diffusivity of a particle evolves randomly in time. In the first class of…

The distribution of the first-passage time (FPT)$T_a$ for a Brownian particle with drift $\mu$ subject to hitting an absorber at a level $a>0$ is well-known and given by its density $\gamma(t) = \frac{a}{\sqrt{2 \pi t^3} } e^{-\frac{(a-\mu…

We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. The construction involves an iteration procedure on an infinite-dimensional…

Evaluating the completion time of a random algorithm or a running stochastic process is a valuable tip not only from a purely theoretical, but also pragmatic point of view. In the formal sense, this kind of a task is specified in terms of…

We consider a non-nestling random walk in a product random environment. We assume an exponential moment for the step of the walk, uniformly in the environment. We prove an invariance principle (functional central limit theorem) under almost…

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…

Advection and dispersion in highly heterogeneous environments involving interfacial discontinuities in the corresponding drift and dispersion rates are described through disparate examples from the physical and biological sciences. A…

We study a one-dimensional anisotropic exclusion process describing particles injected at the origin, moving to the right on a chain of $L$ sites and being removed at the (right) boundary. We construct the steady state and compute the…

In this paper, we introduce and investigate a class P of continuous and periodic functions on R. The class P is defined so that second-order central differences of a function satisfy some concavity-type estimate. Although this definition…

We study the transport properties of a system of active particles moving at constant speed in an heterogeneous two-dimensional space. The spatial heterogeneity is modeled by a random distribution of obstacles, which the active particles…

We consider a positive recurrent one-dimensional diffusion process with continuous coefficients and we establish stable central limit theorems for a certain type of additive functionals of this diffusion. In other words we find some…