May 11, 2012
Location: Janskerkhof 15a (Utrecht), room 101
Random walks in (dynamic) random environments
Random walks in random environments arise when the transition kernels of simple random walks are modified according to a random environment. This modification is dependent on the position of the walk in the environment, which makes the study of the random walk non-trivial. The environment can be either static or dynamic in time. I will give an overview of the topic, presenting both traditional and new results.
In this lecture I present recent results on the extremes for a process where correlations just begin to get noticeable: branching Brownian motion. It has been known from the work of Bramson in the 80s that the distribution of the maximum of BBM is not a standard extremal distribution. I will review some classical results and present some rather new results on the asymptotics of the point process of its extremes.