86 citations · 418 across the 38 of their papers we have counts for
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First pair coalescence among three geodesics
Arjun Krishnan, Firas Rassoul-Agha, Timo Seppäläinen
In directed last-passage percolation with i.i.d. exponential vertex weights, the coalescence time of two semi-infinite geodesics started from vertices $a…
Coalescence and fluctuations of O'Connell$\unicode{x2013}$Yor polymers via the free-energy correlation profile
Firas Rassoul-Agha, Xiao Shen, Ruixuan Zhang +1
We establish an identity relating the spatial derivative of a two-point free-energy correlation to two fundamental geometric quantities: the annealed probability that two independe…
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…
The Martin boundary of the Directed Landscape
Firas Rassoul-Agha, Mikhail Sweeney
In the directed landscape, the Martin boundary coincides with the horofunction boundary. We show that functions in this boundary are precisely the eternal solutions possessing a sp…
Shocks, instability, and the twenty networks of infinite geodesics in the Directed Landscape
Firas Rassoul-Agha, Mikhail Sweeney
For stochastic Hamilton-Jacobi (SHJ) equations, instability points are the space-time locations where two eternal solutions with the same asymptotic velocity differ. Another fundam…
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.…
Shocks and instability in Brownian last-passage percolation
Firas Rassoul-Agha, Mikhail Sweeney
For stochastic Hamilton-Jacobi (SHJ) equations, instability points are the space-time locations where two eternal solutions with the same asymptotic velocity differ. Another crucia…
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…
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…
Coalescence and total-variation distance of semi-infinite inverse-gamma polymers
Firas Rassoul-Agha, Timo Seppäläinen, Xiao Shen
We show that two semi-infinite positive temperature polymers coalesce on the scale predicted by KPZ (Kardar-Parisi-Zhang) universality. The two polymer paths have the same asymptot…
Ergodicity and synchronization of the Kardar-Parisi-Zhang equation
Christopher Janjigian, Firas Rassoul-Agha, Timo Seppäläinen
The Kardar-Parisi-Zhang (KPZ) equation on the real line is well-known to admit Brownian motion with a linear drift as a stationary distribution (modulo additive constants). We show…
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…
Non-existence of non-trivial bi-infinite geodesics in Geometric Last Passage Percolation
Sean Groathouse, Christopher Janjigian, Firas Rassoul-Agha
We show non-existence of non-trivial bi-infinite geodesics in the solvable last-passage percolation model with i.i.d. geometric weights. This gives the first example of a model wit…
Geodesic length and shifted weights in first-passage percolation
Arjun Krishnan, Firas Rassoul-Agha, Timo Seppäläinen
We study first-passage percolation through related optimization problems over paths of restricted length. The path length variable is in duality with a shift of the weights. This p…
A shape theorem and a variational formula for the quenched Lyapunov exponent of random walk in a random potential
Christopher Janjigian, Sergazy Nurbavliyev, Firas Rassoul-Agha
We prove a shape theorem and derive a variational formula for the limiting quenched Lyapunov exponent and the Green's function of random walk in a random potential on a square latt…
Geometry of geodesics through Busemann measures in directed last-passage percolation
Christopher Janjigian, Firas Rassoul-Agha, Timo Seppäläinen
We consider planar directed last-passage percolation on the square lattice with general i.i.d. weights and study the geometry of the full set of semi-infinite geodesics in a typica…
Busemann functions and semi-infinite O'Connell-Yor polymers
Tom Alberts, Firas Rassoul-Agha, Mackenzie Simper
We prove that given any fixed asymptotic velocity, the finite length O'Connell-Yor polymer has an infinite length limit satisfying the law of large numbers with this velocity. By a…
Uniqueness and ergodicity of stationary directed polymers on
Christopher Janjigian, Firas Rassoul-Agha
We study the ergodic theory of stationary directed nearest-neighbor polymer models on , with i.i.d. weights. Such models are equivalent to specifying a stationary dist…
Busemann functions and Gibbs measures in directed polymer models on
Christopher Janjigian, Firas Rassoul-Agha
We consider random walk in a space-time random potential, also known as directed random polymer measures, on the planar square lattice with nearest-neighbor steps and general i.i.d…
Busemann functions, geodesics, and the competition interface for directed last-passage percolation
Firas Rassoul-Agha
In this survey article we consider the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices,…
Large deviations and wandering exponent for random walk in a dynamic beta environment
Márton Balázs, Firas Rassoul-Agha, Timo Seppäläinen
Random walk in a dynamic i.i.d. beta random environment, conditioned to escape at an atypical velocity, converges to a Doob transform of the original walk. The Doob-transformed env…
Averaged vs. quenched large deviations and entropy for random walk in a dynamic random environment
Firas Rassoul-Agha, Timo Seppäläinen, Atilla Yilmaz
We consider random walk with bounded jumps on a hypercubic lattice of arbitrary dimension in a dynamic random environment. The environment is temporally independent and spatially t…
Geodesics and the competition interface for the corner growth model
Nicos Georgiou, Firas Rassoul-Agha, Timo Seppäläinen
We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exac…
Stationary cocycles and Busemann functions for the corner growth model
Nicos Georgiou, Firas Rassoul-Agha, Timo Seppäläinen
We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside of the class of ex…