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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

Pfaffian Schur processes and last passage percolation in a half-quadrant

- J. Baik, Guillaume Barraquand, Ivan Corwin, T. Suidan
- MathematicsThe Annals of Probability
- 2 June 2016

We study last passage percolation in a half-quadrant, which we analyze within the framework of Pfaffian Schur processes. For the model with exponential weights, we prove that the fluctuations of the… Expand

Facilitated exclusion process

- J. Baik, Guillaume Barraquand, Ivan Corwin, T. Suidan
- Mathematics
- 16 August 2016

We study the Facilitated TASEP, an interacting particle system on the one dimensional integer lattice. We prove that starting from step initial condition, the position of the rightmost particle has… Expand

HALF-SPACE MACDONALD PROCESSES

- Guillaume Barraquand, A. Borodin, Ivan Corwin
- MathematicsForum of Mathematics, Pi
- 22 February 2018

Macdonald processes are measures on sequences of integer partitions built using the Cauchy summation identity for Macdonald symmetric functions. These measures are a useful tool to uncover the… Expand

The $q$-Hahn asymmetric exclusion process

- Guillaume Barraquand, Ivan Corwin
- Mathematics
- 14 January 2015

We introduce new integrable exclusion and zero-range processes on the one-dimensional lattice that generalize the $q$-Hahn TASEP and the $q$-Hahn Boson (zero-range) process introduced in [Pov13] and… Expand

Large deviations for sticky Brownian motions

- Guillaume Barraquand, M. Rychnovsky
- Mathematics
- 24 May 2019

We consider n-point sticky Brownian motions: a family of n diffusions that evolve as independent Brownian motions when they are apart, and interact locally so that the set of coincidence times has… Expand

Moderate deviations for diffusion in time dependent random media

- Guillaume Barraquand, P. le Doussal
- PhysicsJournal of Physics A: Mathematical and…
- 23 December 2019

The position x(t) of a particle diffusing in a one-dimensional uncorrelated and time dependent random medium is simply Gaussian distributed in the typical direction, i.e. along the ray x = v 0 t,… Expand

Steady state of the KPZ equation on an interval and Liouville quantum mechanics

- Guillaume Barraquand, P. le Doussal
- MathematicsEPL (Europhysics Letters)
- 31 May 2021

We obtain a simple formula for the stationary measure of the height field evolving according to the Kardar-Parisi-Zhang equation on the interval with general Neumann-type boundary conditions and any… Expand

A short proof of a symmetry identity for the $q$-Hahn distribution

- Guillaume Barraquand
- Mathematics
- 8 February 2014

We give a short and elementary proof of a symmetry identity for the $q$-moments of the $q$-Hahn distribution arising in the study of the $q$-Hahn Boson process and the $q$-Hahn TASEP. This identity… Expand

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