Some results concerning certain solvable directed polymer models and non-linear stochastic partial differential equations.

摘要

This dissertation is broken into two essentially unrelated chapters. The first chapter considers exact computations of large deviation rate functions in various solvable 1+1 dimensional directed polymer models. The models considered include point-to-point and stationary versions of an inhomogeneous directed last passage percolation model, the O'Connell-Yor polymer, and the Brownian directed percolation model. The work on the inhomogeneous corner growth model is joint with Elnur Emrah. The second chapter deals with particle representations for a class of nonlinear stochastic partial differential equations and is based on joint work with Dan Crisan and Tom Kurtz.