3 papers
math.PR2025
Jointly invariant measures for the Kardar-Parisi-Zhang Equation
Sean Groathouse, Firas Rassoul-Agha, Timo Seppäläinen +1
We give an explicit description of the jointly invariant measures for the KPZ equation. These are couplings of Brownian motions with drift, and can be extended to a process defined…
math.PR2025
Large deviations of geodesic midpoint fluctuations in last-passage percolation with general i.i.d. weights
Tom Alberts, Riddhipratim Basu, Sean Groathouse +1
The study of transversal fluctuations of the optimal path is a crucial aspect of the Kardar-Parisi-Zhang (KPZ) universality class. In this work, we establish the large deviation li…
math.PR2025
Existence of generalized Busemann functions and Gibbs measures for random walks in random potentials
Sean Groathouse, Christopher Janjigian, Firas Rassoul-Agha
We establish the existence of generalized Busemann functions and Gibbs-Dobrushin-Landford-Ruelle measures for a general class of lattice random walks in random potential with finit…