Research Overview
My work is in probability theory, with a focus on models of random walks in disordered environments and random growth. KPZ models in 1+1 dimensions are a main source of examples. I am also interested in related stochastic partial differential equations. There are three main themes to my work: (i) the general structure of random walks in random potentials, with a focus on their infinite volume structure; (ii) exactly solvable KPZ models, and (iii) related questions on the ergodic theory of related stochastic partial differential equations. The links below contain links to my papers, organized by theme.
Research Themes
Topic
General Random Walks in
Random Potentials
Random walks in random potentials, first-passage percolation, and infinite-volume structure.
Topic
Solvable KPZ Models
Exactly solvable examples of the types of phenomena in the first project.
Topic
Stochastic PDE and Continuum Models
KPZ, continuum polymers, and related probabilistic approaches to stochastic equations.
This material above is partially based upon work supported by the Simons Foundation Grant MPS-TSM-00012155 and the National Science Foundation under Grant No. DMS-2125961. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation or the Simons Foundation.