91 citations · 792 across the 40 of their papers we have counts for
41 papers
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…
Intertwining the Busemann process of the directed polymer model
Erik Bates, Wai-Tong Louis Fan, Timo Seppäläinen
We study the Busemann process and competition interfaces of the planar directed polymer model with i.i.d.\ weights on the vertices of the planar square lattice, in both the general…
The Green's function of the parabolic Anderson model and the continuum directed polymer
Tom Alberts, Christopher Janjigian, Firas Rassoul-Agha +1
We build a regular version of the field which describes the Green's function, or fundamental solution, of the parabolic Anderson model (PAM) with white noise forcing…
The stationary horizon and semi-infinite geodesics in the directed landscape
Ofer Busani, Timo Seppäläinen, Evan Sorensen
The stationary horizon (SH) is a stochastic process of coupled Brownian motions indexed by their real-valued drifts. It was first introduced by the first author as the diffusive sc…
Global structure of semi-infinite geodesics and competition interfaces in Brownian last-passage percolation
Timo Seppäläinen, Evan Sorensen
In Brownian last-passage percolation (BLPP), the Busemann functions are indexed by two points $\mathbf x,\mathbf y \in \mathbb Z \times \mathbb…
Optimal-order exit point bounds in exponential last-passage percolation via the coupling technique
Elnur Emrah, Christopher Janjigian, Timo Seppäläinen
We develop a new probabilistic method for deriving deviation estimates in directed planar polymer and percolation models. The key estimates are for exit points of geodesics as they…