• Corpus ID: 254275263

Sausage Volume of the Random String and Survival in a medium of Poisson Traps

  title={Sausage Volume of the Random String and Survival in a medium of Poisson Traps},
  author={Siva Athreya and Mathew Joseph and Carl Mueller},
. We provide asymptotic bounds on the survival probability of a moving polymer in an environment of Poisson traps. Our model for the polymer is the vector-valued solution of a stochastic heat equation driven by additive spacetime white noise; solutions take values in R d , d ≥ 1. We give upper and lower bounds for the survival probability in the cases of hard and soft obstacles. Our bounds decay exponentially with rate proportional to T d/ ( d +2) , the same exponent that occurs in the case of… 



The Parabolic Anderson Model: Random Walk in Random Potential

This is a comprehensive survey on the research on the parabolic Anderson model the heat equation with random potential or the random walk in random potential of the years 1990 2015. The investigation

On the chaotic character of the stochastic heat equation, before the onset of intermitttency

We consider a nonlinear stochastic heat equation @tu = 1 @xxu + (u)@xtW , where @xtW denotes space-time white noise and : R ! R is Lipschitz continuous. We establish that, at every xed time t > 0,

Moderate deviations for the volume of the Wiener sausage

For a > 0, let Wa(t) be the a-neighbourhood of standard Brownian motion in Rd starting at 0 and observed until time t. It is well-known that ElWa(t)l IKat (t -> oc) for d > 3, with Kea the Newtonian

Brownian motion, obstacles, and random media

This book is aimed at graduate students and researchers. It provides an account for the non-specialist of the circle of ideas, results and techniques, which grew out in the study of Brownian motion

Random Walk Among Mobile/Immobile Traps: A Short Review

There have been extensive studies of a random walk among a field of immobile traps (or obstacles), where one is interested in the probability of survival as well as the law of the random walk

On the Volume of the Wiener Sausage

Let $W(t, \varepsilon)$ be the $\varepsilon$-Wiener sausage, i.e., the $\varepsilon$-neighborhood of the trace of the Brownian motion up to time $t$. It is shown that the results of Donsker and

Different types of spdes in the eyes of girsanov's theorem

We prove Girsanov's theorem for continuous orthogonal martingale measures. We then define space-time SDEs, and use Girsanov's theorem to establish a oneto- one correspondence between solutions of two

Small ball probabilities and a support theorem for the stochastic heat equation

We consider the following stochastic partial differential equation on $t \geq 0, x\in[0,J], J \geq 1$ where we consider $[0,J]$ to be the circle with end points identified: \begin{equation*}

École d'été de probabilités de Saint Flour XIV, 1984

Random schrodinger operators.- Aspects of first passage percolation.- An introduction to stochastic partial differential equations.