5 papers
Rooted Gibbs-DLR Measures in Planar Directed Polymers
Christopher Janjigian, Firas Rassoul-Agha, Timo Seppäläinen
We study rooted Gibbs-DLR measures in the directed polymer model on with an ergodic disorder distribution which satisfies an additional mild hypothesis. We prove tha…
Strong existence and uniqueness of the tilt-indexed Busemann process in the planar corner growth model
Christopher Janjigian, Firas Rassoul-Agha, Timo Seppäläinen
We show that the Busemann process indexed by tilts in the super-differential of the limit shape exists and is unique in the strong sense in the i.i.d.\ planar corner growth model.…
Anomalous geodesics in the inhomogeneous corner growth model
Elnur Emrah, Christopher Janjigian, Timo Seppäläinen
We study Busemann functions, semi-infinite geodesics, and competition interfaces in the exactly solvable last-passage percolation with inhomogeneous exponential weights. New phenom…
Estimates for the empirical distribution along a geodesic in first-passage percolation
Michael Damron, Jack Hanson, Christopher Janjigian +2
In first-passage percolation, we assign i.i.d.~nonnegative weights to the nearest-neighbor edges of and study the induced pseudometric . In this…
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…