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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

## Macdonald processes

- A. Borodin, Ivan Corwin
- Mathematics
- 18 November 2011

Macdonald processes are probability measures on sequences of partitions defined in terms of nonnegative specializations of the Macdonald symmetric functions and two Macdonald parameters $$q,t \in… Expand

## Brownian Gibbs property for Airy line ensembles

- Ivan Corwin, A. Hammond
- Mathematics
- 10 August 2011

Consider a collection of N Brownian bridges $B_{i}:[-N,N] \to \mathbb{R} $, Bi(−N)=Bi(N)=0, 1≤i≤N, conditioned not to intersect. The edge-scaling limit of this system is obtained by taking a weak… Expand

## From duality to determinants for q-TASEP and ASEP

- A. Borodin, Ivan Corwin, T. Sasamoto
- Mathematics
- 20 July 2012

We prove duality relations for two interacting particle systems: the $q$-deformed totally asymmetric simple exclusion process ($q$-TASEP) and the asymmetric simple exclusion process (ASEP).… Expand

## Stochastic six-vertex model

- A. Borodin, Ivan Corwin, V. Gorin
- Mathematics
- 24 July 2014

We study the asymmetric six-vertex model in the quadrant with parameters on the stochastic line. We show that the random height function of the model converges to an explicit deterministic limit… Expand

## Stochastic Higher Spin Vertex Models on the Line

- Ivan Corwin, L. Petrov
- Mathematics
- 25 February 2015

We introduce a four-parameter family of interacting particle systems on the line, which can be diagonalized explicitly via a complete set of Bethe ansatz eigenfunctions, and which enjoy certain… Expand

## Random-walk in Beta-distributed random environment

- Guillaume Barraquand, Ivan Corwin
- Mathematics
- 13 March 2015

We introduce an exactly-solvable model of random walk in random environment that we call the Beta RWRE. This is a random walk in $$\mathbb {Z}$$Z which performs nearest neighbour jumps with… Expand

## Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension

- A. Borodin, Ivan Corwin, P. Ferrari
- Mathematics
- 4 April 2012

We consider two models for directed polymers in space‐time independent random media (the O'Connell‐Yor semidiscrete directed polymer and the continuum directed random polymer) at positive temperature… 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

## KPZ line ensemble

- Ivan Corwin, A. Hammond
- Mathematics
- 9 December 2013

For each $$t\ge 1$$t≥1 we construct an $$\mathbb {N}$$N-indexed ensemble of random continuous curves with three properties:(1)the lowest indexed curve is distributed as the time t Hopf–Cole solution… Expand

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