This is joint work with Siva Athreya and Mathew Joseph.

A classic question about Brownian motion deals with survival probabilities for the Brownian motion moving among a Poisson field of random obstacles. The process dies when it hits one of the obstacles.

Moving polymers can be modeled using the stochastic heat equation. Motivated by the Brownian case, we study survival probabilities for the moving polymer among random obstacles. Because a solution to the stochastic heat equation is an infinite-dimensional processes, most of the tools used in the Brownian case are not available. We get results in the so-called annealed case, where we do not condition on the obstacles.

This is part of a program to carry over results for finite-dimensional processes to the infinite dimensional setting, which often requires new tools.