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Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions
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}…
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Intermediate disorder regime for directed polymers in dimension 1+1.
TLDR
A new disorder regime for directed polymers in dimension 1+1 is introduced by scaling the inverse temperature β with the length of the polymer n and interpolating between the weak disorder (β=0) and strong disorder regimes (β>0).
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Diffusion in Disordered Media
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…
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Diffusion of color in the simple exclusion process
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…
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The Continuum Directed Random Polymer
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…
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Diffusion processes in composite porous media and their numerical integration by random walks: Generalized stochastic differential equations with discontinuous coefficients
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…
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The KPZ fixed point
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…
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A CLASS OF GROWTH MODELS RESCALING TO KPZ
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…
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Continuum Statistics of the Airy2 Process
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…
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Introduction to KPZ
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…
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