24 citations · 110 across the 18 of their papers we have counts for
18 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…
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…
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…
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…
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…
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…
Right-tail moderate deviations in the exponential last-passage percolation
Elnur Emrah, Chris Janjigian, Timo Seppäläinen
We study moderate deviations in the exponential corner growth model, both in the bulk setting and the increment-stationary setting. The main results are sharp right-tail bounds on…
Flats, spikes and crevices: the evolving shape of the inhomogeneous corner growth model
Elnur Emrah, Christopher Janjigian, Timo Seppäläinen
We study the macroscopic evolution of the growing cluster in the exactly solvable corner growth model with independent exponentially distributed waiting times. The rates of the exp…
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…
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…
Upper tail large deviations in Brownian directed percolation
Christopher Janjigian
This paper presents a new, short proof of the computation of the upper tail large deviation rate function for the Brownian directed percolation model. Through a distributional equi…
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…
Particle representations for stochastic partial differential equations with boundary conditions
Dan Crisan, Christopher Janjigian, Thomas G. Kurtz
In this article, we study a weighted particle representation for a class of stochastic partial differential equations with Dirichlet boundary conditions. The locations and weights…
Large deviations of the free energy in the O'Connell-Yor polymer
Chris Janjigian
We investigate large deviations of the free energy in the O'Connell-Yor polymer through a variational representation of the positive real moment Lyapunov exponents of the associate…