Let B_s be a d-dimensional Brownian motion and ω(dx) be an independent Poisson field on
R^d. The almost sure asymptotics for the logarithmic moment generating function …

A method known as renormalization is proposed for constructing some more physically
realistic random potentials in a Poisson cloud. The Brownian motion in the renormalized …

In (Chen and Kulik, 2009), a method of renormalization was proposed for constructing some
more physically realistic random potentials in a Poisson cloud. This paper is devoted to the …

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 …

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 …

This is a survey of the parabolic Anderson model (PAM), the Cauchy problem for the heat
equation with random potential. This model and many variants and related models are …

V ω (Zs) ds)] associated with a pure-jump symmetric Lévy process (Zt) t⩾ 0 in general
Poissonian random potentials V ω on Rd, which is closely related to the large time …

A quenched large deviation principle for Brownian motion in a stationary potential is proved.
As the proofs are based on a method developed by Sznitman [Comm. Pure Appl. Math. 47 …

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 …

Consider a d-dimensional Brownian motion in a random potential defined by attaching a
nonnegative and polynomially decaying potential around Poisson points. We introduce a …