Conditioned random walks
The random walk is a fundamental model in statistical physics for which many results are known, for example, the linear growth of the mean-square displacement over time. Sometimes we are interested in problems where the walk is constrained to reach a certain point (a target) after a certain amount of time. The statistics of the conditioned ensemble (i.e., the subset of walks that actually hit the desired target) is different from that of unconditioned (free) random walks. In this talk, I will explain why I am interested in this problem, rattle through a few approaches for studying the conditioned ensemble, and try and show some results.
This is a weekly series of informal talks focussing on some theoretical aspect of Condensed Matter, Biological, and Statistical Physics..