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Existence of Hydrodynamics for the Totally Asymmetric Simple K-Exclusion Process

- T. Seppäläinen
- Mathematics
- 1999

In a totally asymmetric simple K-exclusion process, particles take nearest-neighbor steps to the right on the lattice Z, under the constraint that each site contain at most K particles. We prove that… Expand

Scaling for a one-dimensional directed polymer with boundary conditions

- T. Seppäläinen
- Mathematics
- 12 November 2009

We study a (1+1)-dimensional directed polymer in a random environment on the integer lattice with log-gamma distributed weights. Among directed polymers, this model is special in the same way as the… Expand

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

Hydrodynamic Profiles for the Totally Asymmetric Exclusion Process with a Slow Bond

- T. Seppäläinen
- Mathematics
- 8 March 2000

We study a totally asymmetric simple exclusion process where jumps happen at rate one, except at the origin where the rate is lower. We prove a hydrodynamic scaling limit to a macroscopic profile… Expand

A MICROSCOPIC MODEL FOR THE BURGERS EQUATION AND LONGEST INCREASING SUBSEQUENCES

- T. Seppäläinen
- Mathematics
- 3 June 1996

We introduce an interacting random process related to Ulam's problem, or finding the limit of the normalized longest increasing subsequence of a random permutation. The process describes the… Expand

Exact limiting shape for a simplified model of first-passage percolation on the plane

- T. Seppäläinen
- Mathematics
- 1 July 1998

We derive the limiting shape for the following model of first-passage bond percolation on the two-dimensional integer lattice: the percolation is directed in the sense that admissible paths are… Expand

The Strict-Weak Lattice Polymer

- Ivan Corwin, T. Seppäläinen, Hao Shen
- Mathematics
- 5 September 2014

We introduce the strict-weak polymer model, and show the KPZ universality of the free energy fluctuation of this model for a certain range of parameters. Our proof relies on the observation that the… Expand

Large deviations for increasing sequences on the plane

- T. Seppäläinen
- Mathematics
- 16 October 1998

Abstract. We prove a large deviation principle with explicit rate functions for the length of the longest increasing sequence among Poisson points on the plane. The rate function for lower tail… Expand

Hydrodynamics and Platoon Formation for a Totally Asymmetric Exclusion Model with Particlewise Disorder

- T. Seppäläinen, J. Krug
- Mathematics
- 1 May 1999

We consider a one-dimensional totally asymmetric exclusion model with quenched random jump rates associated with the particles, and an equivalent interface growth process on the square lattice. 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

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