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Right-tail moderate deviations in the exponential last-passage percolation.

- Elnur Emrah, Christopher Janjigian, T. Seppalainen
- Mathematics
- 8 April 2020

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 the last-passage… Expand

Optimal-order exit point bounds in exponential last-passage percolation via the coupling technique

- Elnur Emrah, Christopher Janjigian, T. Seppalainen
- Mathematics
- 19 May 2021

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 cross transversal… Expand

A shape theorem and a variational formula for the quenched Lyapunov exponent of random walk in a random potential

- Christopher Janjigian, Sergazy Nurbavliyev, F. Rassoul-Agha
- MathematicsAnnales de l'Institut Henri Poincaré, Probabilit…
- 18 June 2020

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 lattice of arbitrary… Expand

Particle representations for stochastic partial differential equations with boundary conditions

- D. Crisan, Christopher Janjigian, T. Kurtz
- Mathematics
- 29 July 2016

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 of the particles… Expand

Large Deviations of the Free Energy in the O’Connell–Yor Polymer

- Christopher Janjigian
- Mathematics
- 2 December 2014

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 associated parabolic… Expand

Geometry of geodesics through Busemann measures in directed last-passage percolation

- Christopher Janjigian, F. Rassoul-Agha, T. Seppalainen
- MathematicsJournal of the European Mathematical Society
- 23 August 2019

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 typical realization of… Expand

Large deviations for some corner growth models with inhomogeneity

- Elnur Emrah, Christopher Janjigian
- Mathematics
- 8 September 2015

We study an inhomogeneous generalization of the classical corner growth in which the weights are exponentially distributed with random parameters. Our main interest is in the quenched and annealed… Expand

Flats, spikes and crevices: the evolving shape of the inhomogeneous corner growth model

- Elnur Emrah, Christopher Janjigian, T. Seppalainen
- Mathematics
- 25 August 2019

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 exponentials are given… Expand

BUSEMANN FUNCTIONS AND GIBBS MEASURES IN DIRECTED POLYMER MODELS ON Z2 BY CHRISTOPHER JANJIGIAN*

- Christopher Janjigian, F. Rassoul-Agha
- Mathematics
- 2019

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. weights on the… Expand

Uniqueness and Ergodicity of Stationary Directed Polymers on $$\mathbb {Z}^2$$

- Christopher Janjigian, F. Rassoul-Agha
- Mathematics
- 20 December 2018

We study the ergodic theory of stationary directed nearest neighbor polymer models on $\mathbb Z^2$, with i.i.d. weights. Such models are equivalent to specifying a stationary distribution on the… Expand

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