Some Curious Properties of Constrained Brownian Motion
This event is part of the Departmental Seminars.
Dissertation Committee: Sid Redner, William Klein, Shyam Erramilli, Martin Schmaltz, Claudio Chamon
Brownian motion and random walks are the Ising models of stochastic processes. The field has been studied to a great depth, but it still continues to surprise us with novel properties. In this talk I will present two related models which are one-step perturbation to the simple Brownian motion process. As a warm up, we will first see some calculations on the statistics of a constrained first passage path. We see how intermediate levels are transited by a Brownian trajectory before reaching the destination level. Using similar tools, we will then tackle the problems of a Brownian forager with greed and a Brownian searcher with reset. We see very non-trivial results in both these cases, for example, little greed being hurtful for a forager in 1-dimension, and too much greed being hurtful in 2-dimensions and so on. I will also speak about their implications to the real-world phenomena in ecology and search problems.