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An almost sure invariance principle for random walks in a space-time random environment

- F. Rassoul-Agha, T. Seppäläinen
- Mathematics
- 26 November 2004

Abstract.We consider a discrete time random walk in a space-time i.i.d. random environment. We use a martingale approach to show that the walk is diffusive in almost every fixed environment. We… Expand

A Course on Large Deviations With an Introduction to Gibbs Measures

- F. Rassoul-Agha, T. Seppäläinen
- Mathematics
- 12 March 2015

Large deviations: General theory and i.i.d. processes Introductory discussion The large deviation principle Large deviations and asymptotics of integrals Convex analysis in large deviation theory… Expand

Variational Formulas and Cocycle solutions for Directed Polymer and Percolation Models

- N. Georgiou, F. Rassoul-Agha, T. Seppäläinen
- Mathematics
- 13 November 2013

We discuss variational formulas for the law of large numbers limits of certain models of motion in a random medium: namely, the limiting time constant for last-passage percolation and the limiting… Expand

The point of view of the particle on the law of large numbers for random walks in a mixing random environment

- F. Rassoul-Agha
- Mathematics
- 17 June 2002

The point of view of the particle is an approach that has proven very powerful in the study of many models of random motions in random media. We provide a new use of this approach to prove the law of… Expand

A Minicourse on Stochastic Partial Differential Equations

- R. Dalang, D. Khoshnevisan, C. Mueller, D. Nualart, Yimin Xiao, F. Rassoul-Agha
- Mathematics
- 21 November 2008

A Primer on Stochastic Partial Differential Equations.- The Stochastic Wave Equation.- Application of Malliavin Calculus to Stochastic Partial Differential Equations.- Some Tools and Results for… Expand

Stationary cocycles and Busemann functions for the corner growth model

- N. Georgiou, F. Rassoul-Agha, T. Seppäläinen
- Mathematics
- 3 October 2015

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 exactly solvable… Expand

Geodesics and the competition interface for the corner growth model

- N. Georgiou, F. Rassoul-Agha, T. Seppäläinen
- Mathematics
- 3 October 2015

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 exactly solvable… Expand

Quenched Free Energy and Large Deviations for Random Walks in Random Potentials

- F. Rassoul-Agha, T. Seppäläinen, A. Yilmaz
- Mathematics
- 15 April 2011

We study quenched distributions on random walks in a random potential on integer lattices of arbitrary dimension and with an arbitrary finite set of admissible steps. The potential can be unbounded… Expand

Ratios of partition functions for the log-gamma polymer

- N. Georgiou, F. Rassoul-Agha, T. Seppalainen, A. Yilmaz
- Mathematics
- 6 March 2013

We introduce a random walk in random environment associated to an underlying directed polymer model in 1 + 1 dimensions. This walk is the positive temperature counterpart of the competition in-… Expand

Large deviations for random walks in a mixing random environment and other (non‐Markov) random walks

- F. Rassoul-Agha
- Mathematics
- 1 September 2004

We extend a recent work by S. R. S. Varadhan [8] on large deviations for random walks in a product random environment to include more general random walks on the lattice. In particular, some… Expand

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