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Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions

- Gideon Amir, Ivan Corwin, J. Quastel
- Mathematics
- 1 March 2010

We consider the solution of the stochastic heat equation $$\partial_T {\cal Z} = {{1}\over{2}} \partial_X^2 {\cal Z} - {\cal Z} \dot{\cal{W}}$$ with delta function initial condition $${\cal Z}… Expand

Intermediate disorder regime for directed polymers in dimension 1+1.

- Tom Alberts, K. Khanin, J. Quastel
- PhysicsPhysical review letters
- 9 March 2010

TLDR

Diffusion in Disordered Media

- J. Quastel
- Mathematics
- 1996

We study the transport properties of a large system of interacting particles moving on an integer lattice in the presence of a random field. This article contains a description of the problem, a… Expand

Diffusion of color in the simple exclusion process

- J. Quastel
- Mathematics
- 1 July 1992

We prove a diffusion scaling limit for the macroscopic densities of colored particles performing the simply excluded random walk, and relate this to the limiting behavior of a test particle in… Expand

The Continuum Directed Random Polymer

- Tom Alberts, K. Khanin, J. Quastel
- Mathematics
- 20 February 2012

Motivated by discrete directed polymers in one space and one time dimension, we construct a continuum directed random polymer that is modeled by a continuous path interacting with a space-time white… Expand

Diffusion processes in composite porous media and their numerical integration by random walks: Generalized stochastic differential equations with discontinuous coefficients

- E. Labolle, J. Quastel, G. Fogg, J. Gravner
- Mathematics
- 1 March 2000

Discontinuities in effective subsurface transport properties commonly arise (l) at abrupt contacts between geologic materials (i.e., in composite porous media) and (2) in discrete velocity fields of… Expand

The KPZ fixed point

- K. Matetski, J. Quastel, Daniel Remenik
- MathematicsActa Mathematica
- 30 December 2016

An explicit Fredholm determinant formula is derived for the multipoint distribution of the height function of the totally asymmetric simple exclusion process with arbitrary initial condition. The… Expand

A CLASS OF GROWTH MODELS RESCALING TO KPZ

- Martin Hairer, J. Quastel
- Mathematics, EconomicsForum of Mathematics, Pi
- 24 December 2015

We consider a large class of $1+1$ -dimensional continuous interface growth models and we show that, in both the weakly asymmetric and the intermediate disorder regimes, these models converge to… Expand

Continuum Statistics of the Airy2 Process

- Ivan Corwin, J. Quastel, Daniel Remenik
- Mathematics
- 14 June 2011

We develop an exact determinantal formula for the probability that the Airy_2 process is bounded by a function g on a finite interval. As an application, we provide a direct proof that… Expand

Introduction to KPZ

- J. Quastel
- Mathematics
- 2011

This is an introductory survey of the Kardar-Parisi-Zhang equation (KPZ). The first chapter provides a non-rigorous background to the equation and to some of the many models which are supposed to lie… Expand

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