Evolution of a passive particle in a one-dimensional diffusive environment

On stationarity of Lagrangian observations of passive tracer velocity in a compressible environment

We study the transport of a passive tracer particle in a steady strongly mixing flow with a nonzero mean velocity. We show that there exists a probability measure under which the particle Lagrangian velocity process is stationary. This measure is absolutely continuous with respect to the underlying probability measure for the Eulerian flow.

Residual Diffusivity in Elephant Random Walk Models with Stops

We study the enhanced diffusivity in the so called elephant random walk model with stops (ERWS) by including symmetric random walk steps at small probability $ε$. At any $ε> 0$, the large time behavior transitions from sub-diffusive at $ε= 0$ to diffusive in a wedge shaped parameter regime where the diffusivity is strictly above that in the un-perturbed ERWS model in the $ε\downarrow 0$ limit. The perturbed ERWS model is shown to be solvable with the first two moments and their asymptotics calculated exactly in both one and two space dimensions. The model provides a discrete analytical setting…

主动-被动排斥过程的水动力学极限

Hydrodynamic limit for an active-passive exclusion process

本文研究主动-被动粒子混合排斥过程的集体非平衡动力学，推导其水动力学方程，并推广非梯度分解与谱隙估计以应对连续取向带来的新挑战。

Directed polymer in $γ$-stable Random Environments

The transition from a weak-disorder (diffusive phase) to a strong-disorder (localized phase) for directed polymers in a random environment is a well studied phenomenon. In the most common setup, it is established that the phase transition is trivial when the transversal dimension $d$ equals $1$ or $2$ (the diffusive phase is reduced to $β=0$) while when $d\geq 3$, there is a critical temperature $β_c\in (0,\infty)$ which delimits the two phases. The proof of the existence of a diffusive regime for $d\geq 3$ is based on a second moment method, and thus relies heavily on the assumption that the …

Transport properties of diffusive particles conditioned to survive in trapping environments

We consider a one-dimensional Brownian motion with diffusion coefficient $D$ in the presence of $n$ partially absorbing traps with intensity $β$, separated by a distance $L$ and evenly spaced around the initial position of the particle. We study the transport properties of the process conditioned to survive up to time $t$. We find that the surviving particle first diffuses normally, before it encounters the traps, then undergoes a period of transient anomalous diffusion, after which it reaches a final diffusive regime. The asymptotic regime is governed by an effective diffusion coefficient $D_…

三维指数混合与随机化ABC流的理想运动学发电机

Three-dimensional exponential mixing and ideal kinematic dynamo with randomized ABC flows

本文研究了三维周期盒中随机化ABC流的拉格朗日性质，证明了其正的最大Lyapunov指数与几何遍历性，并据此论证了该流场对被动标量是指数混合场，且为被动向量提供了普适理想运动学发电机实例。

Random walks in space time mixing environments

We prove that random walks in random environments, that are exponentially mixing in space and time, are almost surely diffusive, in the sense that their scaling limit is given by the Wiener measure.