相关论文: Localization of favorite points for diffusion in r…

Let $\tau = (\tau_i : i \in {\Bbb Z})$ denote i.i.d.~positive random variables with common distribution $F$ and (conditional on $\tau$) let $X = (X_t : t\geq0, X_0=0)$, be a continuous-time simple symmetric random walk on ${\Bbb Z}$ with…

Many events in biology are triggered when a diffusing searcher finds a target, which is called a first passage time (FPT). The overwhelming majority of FPT studies have analyzed the time it takes a single searcher to find a target. However,…

The self-diffusion process of a hard sphere fluid confined by two parallel plates separated by a distance on the order of the particle diameter is studied. The starting point is a closed kinetic equation for the distribution function that…

Combining experiments and theory, we address the dynamics of self-propelled particles in crowded environments. We first demonstrate that motile colloids cruising at constant speed through random lattices undergo a smooth transition from…

This paper deals with the numerical modeling of wave propagation in porous media described by Biot's theory. The viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity, which…

In this paper we look at the properties of limits of a sequence of real valued time inhomogeneous diffusions. When convergence is only in the sense of finite-dimensional distributions then the limit does not have to be a diffusion. However,…

We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…

We study the voter model and related random-copying processes on arbitrarily complex network structures. Through a representation of the dynamics as a particle reaction process, we show that a quantity measuring the degree of order in a…

Let $(X_t)$ be a reflected diffusion process in a bounded convex domain in $\mathbb R^d$, solving the stochastic differential equation $$dX_t = \nabla f(X_t) dt + \sqrt{2f (X_t)} dW_t, ~t \ge 0,$$ with $W_t$ a $d$-dimensional Brownian…

We consider the Halfin-Whitt diffusion process $X_d(t)$, which is used, for example, as an approximation to the $m$-server $M/M/m$ queue. We use recently obtained integral representations for the transient density $p(x,t)$ of this diffusion…

Molecules in dense environments, such as biological cells, are subjected to forces that fluctuate both in time and in space. While spatial fluctuations are captured by Lifson-Jackson-Zwanzig's model of "diffusion in a rough potential", and…

We have random number of independent diffusion processes with absorption on boundaries in some region at initial time $t=0$. The initial numbers and positions of processes in region is defined by Poisson random measure. It is required to…

A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model,…

A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…

The fast diffusion equation is analyzed on a bounded domain with Dirichlet boundary conditions, for which solutions are known to extinct in finite time. We construct invariant manifolds that provide a finite-dimensional approximation near…

We consider diffusion processes x_{t} on the unit interval. Doob-transformation techniques consist of a selection of x_{t}-paths procedure. The law of the transformed process is the one of a branching diffusion system of particles, each…

Suppose $X$ is a multidimensional diffusion process. Assume that at time zero the state of $X$ is fully observed, but at time $T>0$ only linear combinations of its components are observed. That is, one only observes the vector $L X_T$ for a…

We investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We examine the well-posedness issue and prove that the space-dependent variable order coefficient is uniquely determined among other…

We prove that multidimensional diffusions in random environment have a limiting velocity which takes at most two different values. Further, in the two-dimensional case we show that for any direction, the probability to escape to infinity in…

Consider "Frozen Random Walk" on $\mathbb{Z}$: $n$ particles start at the origin. At any discrete time, the leftmost and rightmost $\lfloor{\frac{n}{4}}\rfloor$ particles are "frozen" and do not move. The rest of the particles in the "bulk"…