109 citations · 512 across the 33 of their papers we have counts for
34 papers
Random walks in Dirichlet random environment in dimension
Guillaume Barraquand, Alexander K. Hartmann, Pierre Le Doussal
The atypical behaviour of random walks in time-dependent random environment was recently related to Kardar-Parisi-Zhang (KPZ) growth. While this is now well-understood in spatial d…
Stationary inverse-Wishart polymers
Guillaume Barraquand, Zikun Ouyang
A solvable model of directed polymer with matrix-valued disorder is introduced in arXiv:2203.14868. The disorder is made of inverse-Wishart random matrices, so that the…
Convergence of the KMP model to the KPZ equation
Guillaume Barraquand, Francesco Casini
We prove that the Kipnis-Marchioro-Presutti (KMP) process converges to the Kardar-Parisi-Zhang (KPZ) equation, as time goes to infinity, in a properly scaled observation window…
Introduction to quantum exclusion processes
Guillaume Barraquand, Denis Bernard
The QSSEP, short for quantum symmetric simple exclusion process, is a paradigm model for stochastic quantum dynamics. Averaging over the noise, the quantum dynamics reduce to the w…
Large time cumulants of the KPZ equation on an interval
Guillaume Barraquand, Pierre Le Doussal
We consider the Kardar-Parisi-Zhang equation on the interval with Neumann type boundary conditions and boundary parameters . We show that the -th order cumulant of…
Integral formulas for two-layer Schur and Whittaker processes
Guillaume Barraquand
Stationary measures of last passage percolation with geometric weights and the log-gamma polymer in a strip of the lattice are characterized in arXiv:2306.05983 using…
KPZ exponents for the half-space log-gamma polymer
Guillaume Barraquand, Ivan Corwin, Sayan Das
We consider the point-to-point log-gamma polymer of length in a half-space with i.i.d. distributed bulk weights and i.i.d. $\operatorname{Gamma…
Stationary measures for integrable polymers on a strip
Guillaume Barraquand, Ivan Corwin, Zongrui Yang
We prove that the stationary measures for the free-energy increment process for the geometric last passage percolation (LPP) and log-gamma polymer model on a diagonal strip is give…
Weakly asymmetric facilitated exclusion process
Guillaume Barraquand, Oriane Blondel, Marielle Simon
We consider the facilitated exclusion process, an interacting particle system on the integer line where particles hop to one of their left or right neighbouring site only when the…
Markov duality and Bethe ansatz formula for half-line open ASEP
Guillaume Barraquand, Ivan Corwin
Using a Markov duality satisfied by ASEP on the integer line, we deduce a similar Markov duality for half-line open ASEP and open ASEP on a segment. This leads to closed systems of…
Stationary measures of the KPZ equation on an interval from Enaud-Derrida's matrix product ansatz representation
Guillaume Barraquand, Pierre Le Doussal
The stationary measures of the Kardar-Parisi-Zhang equation on an interval have been computed recently. We present a rather direct derivation of this result by taking the weak asym…
A stationary model of non-intersecting directed polymers
Guillaume Barraquand, Pierre Le Doussal
We consider the partition function of non-intersecting continuous directed polymers of length in dimension , in a white noise env…
Stationary measures for the log-gamma polymer and KPZ equation in half-space
Guillaume Barraquand, Ivan Corwin
We construct explicit one-parameter families of stationary measures for the Kardar-Parisi-Zhang equation in half-space with Neumann boundary conditions at the origin, as well as fo…
Half-space stationary Kardar-Parisi-Zhang equation beyond the Brownian case
Guillaume Barraquand, Alexandre Krajenbrink, Pierre Le Doussal
We study the Kardar-Parisi-Zhang equation on the half-line with Neumann type boundary condition. Stationary measures of the KPZ dynamics were characterized in recen…
Random walk on nonnegative integers in beta distributed random environment
Guillaume Barraquand, Mark Rychnovsky
We consider random walks on the nonnegative integers in a space-time dependent random environment. We assume that transition probabilities are given by independent $\mathrm{Beta}(μ…
An identity in distribution between full-space and half-space log-gamma polymers
Guillaume Barraquand, Shouda Wang
We prove an identity in distribution between two kinds of partition functions for the log-gamma directed polymer model: (1) the point-to-point partition function in a quadrant, (2)…
Steady state of the KPZ equation on an interval and Liouville quantum mechanics
Guillaume Barraquand, Pierre Le Doussal
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 b…
Maximal free energy of the log-gamma polymer
Guillaume Barraquand, Ivan Corwin, Evgeni Dimitrov
We prove a phase transition for the law of large numbers and fluctuations of , the maximum of the free energy of the log-gamma directed polymer with parameter , max…
The KPZ equation in a half space with flat initial condition and the unbinding of a directed polymer from an attractive wall
Guillaume Barraquand, Pierre Le Doussal
We present an exact solution for the height distribution of the KPZ equation at any time in a half space with flat initial condition. This is equivalent to obtaining the free e…
Spatial tightness at the edge of Gibbsian line ensembles
Guillaume Barraquand, Ivan Corwin, Evgeni Dimitrov
Consider a sequence of Gibbsian line ensembles, whose lowest labeled curves (i.e., the edge) have tight one-point marginals. Then, given certain technical assumptions on the nature…
Fluctuations of the log-gamma polymer free energy with general parameters and slopes
Guillaume Barraquand, Ivan Corwin, Evgeni Dimitrov
We prove that the free energy of the log-gamma polymer between lattice points and converges to the GUE Tracy-Widom distribution in the scaling, provided t…
Half-space stationary Kardar-Parisi-Zhang equation
Guillaume Barraquand, Alexandre Krajenbrink, Pierre Le Doussal
We study the solution of the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an interface of height on the positive half line, equivalently the free energy…
Moderate deviations for diffusion in time dependent random media
Guillaume Barraquand, Pierre Le Doussal
The position 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 t…
Stochastic growth in time dependent environments
Guillaume Barraquand, Pierre Le Doussal, Alberto Rosso
We study the Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with a noise variance depending on time. We find that for there is a transition…