Limit Theorems for the Minimal Position of a Branching Random Walk in Random Environment

摘要

We consider a branching system of N-valued random walks with a random environment in location. We will give the exact limit value of M-n, where M-n denotes the minimal position of the branching random walk at time n. A key step in the proof is to transfer our branching random walks with a random environment in location to branching random walks with a random environment in time, by use of Bramson's "branching processes within a branching process" (1978).