Related papers: Quenched asymptotics for Brownian motion in genera…
Let $B_s$ be a $d$-dimensional Brownian motion and $\omega(dx)$ be an independent Poisson field on $\mathbb{R}^d$. The almost sure asymptotics for the logarithmic moment generating function [\log\math…
A quenched large deviation principle for Brownian motion in a non-negative, stationary potential is proved. A sufficient moment condition on the potential is given but unlike the results of Armstrong and Tran (2014) no regularity is…
Let $B_s$ be a three dimensional Brownian motion and $\omega(dx)$ be an independent Poisson field on $\mathbb{R}^3$. It is proved that for any $t>0$, conditionally on $\omega(\cdot)$, \label{*} \mathbb{E}_0 \exp\{\theta \int_0^t…
We establish explicit quenched asymptotics for pure-jump symmetric L\'evy processes in general Poissonian potentials, which is closely related to large time asymptotic behavior of solutions to the nonlocal parabolic Anderson problem with…
We determine the asymptotic relaxation rate of a Brownian particle in a harmonic potential perturbed by quenched Gaussian disorder, a simplified model for rugged energy landscapes in complex systems. Depending on the properties of the…
We study the quenched long time behaviour of the survival probability up to time $t$, $\mathbf{E}_x\big[e^{-\int_0^t V^{\omega}(X_s){\rm d}s}\big],$ of a symmetric L\'evy process with jumps, under a sufficiently regular Poissonian random…
We study a spatial branching model, where the underlying motion is $d$-dimensional ($d\ge1$) Brownian motion and the branching rate is affected by a random collection of reproduction suppressing sets dubbed mild obstacles. The main result…
We consider the Feynman-Kac functional associated with a Brownian motion in a random potential. The potential is defined by attaching a heavy tailed positive potential around the Poisson point process. This model was first considered by…
A generalized Einstein relation is studied for Brownian motion in a tilted potential. The exact form of the diffusion constant of the Brownian motion is compared with the generalized Einstein relation. The generalized Einstein relation is a…
We derive asymptotics for the quenched probability that a critical branching Brownian motion killed at a small rate in Poissonian obstacles exits a large domain. Results are formulated in terms of the solution to a semilinear partial…
The dynamics of a Brownian particle in a constant magnetic field and time-dependent electric field is studied in the limit of white noise, using a Langevin approach for the classical problem and the path-integral Feynman-Vernon and…
Motivated by the study of the directed polymer model with mobile Poissonian traps or catalysts and the stochastic parabolic Anderson model with time dependent potential, we investigate the asymptotic behavior of…
Brownian motion, as one of the most fundamental concepts in statistical physics, has everlasting interests in interdisciplinary fields in the past century. Although this motion with static potentials have been widely explored, its physics…
We give an exact solution to the generalized Langevin equation of motion of a charged Brownian particle in a uniform magnetic field that is driven internally by an exponentially-correlated stochastic force. A strong dissipation regime is…
We prove a quenched local central limit theorem for continuous-time random walks in $\mathbb Z^d, d\ge 2$, in a uniformly-elliptic time-dependent balanced random environment which is ergodic under space-time shifts. We also obtain Gaussian…
In this paper, long time and high order moment asymptotics for super-Brownian motions (sBm's) are studied. By using a moment formula for sBm's (e.g. Theorem 3.1, Hu et al. Ann. Appl. Probab. 2023+), precise upper and lower bounds for all…
We begin with a review and analytical construction of quantum Gaussian process (and quantum Brownian motions) in the sense of [25],[10] and others, and then formulate and study in details (with a number of interesting examples) a definition…
We extend to the vector-valued situation some earlier work of Ciesielski and Roynette on the Besov regularity of the paths of the classical Brownian motion. We also consider a Brownian motion as a Besov space valued random variable. It…
Brownian motion is a central scientific paradigm. Recently, due to increasing efforts and interests towards miniaturization and small-scale physics or biology, the effects of confinement on such a motion have become a key topic of…
We study the motion of a random walker in one longitudinal and d transverse dimensions with a quenched power law correlated velocity field in the longitudinal x-direction. The model is a modification of the Matheron-de Marsily (MdM) model,…