General Random Walks in Random Potentials

One of my main research areas concerns non-solvable models of random walks in random potentials. This broad class of models encompasses first- and last-passage percolation, directed polymers in random environments, and random walks in random potentials. Many of the questions I am interested in concern infinite-volume structure, with a focus on developing tools that generalize beyond exactly solvable settings.

Relevant Papers

Co-authors	Citation	Links
Firas Rassoul-Agha Timo Seppäläinen	Strong existence and uniqueness of the tilt-indexed Busemann process in the planar corner growth model. (2025).	arXiv
Michael Damron Jack Hanson Wai-Kit Lam Xiao Shen	Estimates for the empirical distribution along a geodesic in first-passage percolation. (2024).	arXiv

Sean Groathouse Firas Rassoul-Agha	Existence of generalized Busemann functions and Gibbs measures for random walks in random potentials. Transactions of the American Mathematical Society, Volume 378, Issue 12, ISSN 1088-6850 (2025).	arXiv Published
Firas Rassoul-Agha Timo Seppäläinen	Geometry of geodesics through Busemann measures in directed last-passage percolation. Journal of the European Mathematical Society 25 (7) 2573-2639 (2023).	arXiv Published
Sergazy Nurbavliyev Firas Rassoul-Agha	A shape theorem and a variational formula for the quenched Lyapunov exponent of random walk in a random potential. Annales de l'Institut Henri Poincare, Probabilites et Statistiques 58(2): 1010-1040 (2022).	arXiv Published
Firas Rassoul-Agha	Uniqueness and ergodicity of stationary directed polymer models on the square lattice. Journal of Statistical Physics 179: 672-689 (2020).	arXiv Published
Firas Rassoul-Agha	Busemann functions and Gibbs measures in directed polymer models on \( \mathbb{Z}^2 \). Annals of Probability 48(2): 778-816 (2020).	Extended Published