2019-02-20
10:15 at HCP F 43.4

Fluctuations of growing interfaces and directed polymers

Sherry Chu

Massachusetts Institute of Technology, Cambridge, MA, United States

Directed polymers in random media (DPRM) is a simple lattice model in the Kardar-Parisi-Zhang (KPZ) universality class for stochastic surface growth. The model considers configurations of a directed path traversing a random energy landscape. Unlike the traveling salesman problem (which allows overhangs and loops), the optimization problem can be solved in polynomial time with a transfer matrix formalism. The optimal path exhibits sample to sample fluctuations, where the energy scales with the path length t as t^1/3, and the transverse wandering scales as t^2/3. In 1+1 dimensions, and for uncorrelated random energies, the scaled probability of these fluctuations satisfies the Tracy-Widom distribution from random matrix theory. Applications of DPRM include the modeling of optimal routes in GPS road networks and of genetic lineages in microbial range expansions.