Physics (Internal)

Greed Could be Dangerous: Statistical physics of Stochastic Search and Lattice Foraging

This event is part of the PhD Final Oral Exams.

Dissertation Committee: Sid Redner, Martin Schmaltz, Shyam Erramilli, Claudio Chamon, Andrei Ruckenstein

Abstract:

Abstract: As the proverbial title suggests, we find surprising results on lifetimes of random-walking lattice foragers. The set-up is as follows. A random-walking forager is initially on an `Eden' lattice filled with food at every-site, which is depleted as the forager hops from site to site. This forager has a limit on how many steps it can go without food, after which, the forager starves to death. It also has the ability to detect food in its nearest neighboring sites. It turns out, acting greedily on this information (i.e., biasing its steps towards nearest neighbors with food), can actually hurt the lifetime of the lattice forager in one and two-dimensions giving rise to a mean-lifetime that depends non-monotonically on such a bias. In a broader context, we study stochastic search and foraging. We use first-passage ideas and develop exact analytic and heuristic tools to study two related systems, one rich with resources and the other where resources are sparse. These models not only serve as simple models of foraging, but also serve as archetypes of non-equilibrium statistical physical processes.