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We survey recent results and open questions on the ballistic phase of stretched polymers in both annealed and quenched random environments
Quenched Lyapunov exponent for the parabolic Anderson model in a dynamic random environment
Quenched Lyapunov exponent parabolic Anderson model
2010/11/9
We continue our study of the parabolic Anderson equation $\partial u/\partial t = \kappa\Delta u + \gamma\xi u$ for the space-time field $u\colon\,\Z^d\times [0,\infty)\to\R$, where $\kappa \in [0,\in...
Convergence in $L^p$ and its exponential rate for a branching process in a random environment
branching process random environment
2010/11/9
We consider a supercritical branching process $(Z_n)$ in a random environment $\xi$. Let $W$ be the limit of the normalized population size $W_n=Z_n/E[Z_n|\xi]$. We first show a necessary and sufficie...