89 citations · 202 across the 20 of their papers we have counts for
26 papers
Bernoulli variables, classical exclusion processes and free probability
Michel Bauer, Denis Bernard, Philippe Biane +1
We present a new description of the known large deviation function of the classical symmetric simple exclusion process by exploiting its connection with the quantum symmetric simpl…
Combinatorics of the Quantum Symmetric Simple Exclusion Process, associahedra and free cumulants
Philippe Biane
The Quantum Symmetric Simple Exclusion Process (QSSEP) is a model of quantum particles hopping on a finite interval and satisfying the exclusion principle. Recently Bernard and Jin…
Mating of discrete trees and walks in the quarter-plane
Philippe Biane
We give a general construction of triangulations starting from a walk in the quarter plane with small steps, which is a discrete version of the mating of trees. We use a special in…
Nonlinear free Lévy-Khinchine formula and conformal mapping
Philippe Biane
There are two natural notions of Lévy processes in free probability: the first one has free increments with homogeneous distributions and the other has homogeneous transition proba…
Laver tables and combinatorics
Philippe Biane
The Laver tables are finite combinatorial objects with a simple elementary definition, which were introduced by R. Laver from considerations of logic and set theory. Although these…
Noncrossing partitions, Bruhat order and the cluster complex
Philippe Biane, Matthieu Josuat-Vergès
We introduce two order relations on finite Coxeter groups which refine the absolute and the Bruhat order, and establish some of their main properties. In particular we study the re…