9 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…
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…
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…
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 , ma…
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…