Julien Barré (Orléans)Jean-Baptiste Gouéré (Tours)
Main fields Statistics is mainly present in Orléans. Probability is present in both sites. Algebra, Combinatorics and Ergodic Theory are present in Tours. Probability, Algebra and Combinatorics are associated in a natural way, in particular because of significative common works of the team on random walks from algebraic, combinatorial and probabilistic point of view.
Statistics Theoretical Statistics, Models and EstimationFunctional statistics Inverse problems Nonparametric and parametric Bayesian Statistics Nonparametric mixture models Statistics for diffusions
Computational Statistics, Data analysis and ApplicationsClassification Clustering (supervised, unsupervised, model-based, functional) Dirichlet models in data analysis. Image Processing (ANR Mistic : 2020-2024) MCMC algorithms Statistical Computing and development of R software packages
Probability Random walks: algebraic, combinatorial and probabilistic aspectsRepresentations theory and conditioned random walks Harmonic functions on graphs Counting paths in lattices Random walks and enumeration of walks in cones Conditioned random walks in Weyl chambers and Pitman transform (Projet académique MADACA (2014-2016)) Martin boundary Random walks in random environment Penalization Random walks in heterogeneous medium Fluctuations of products of random matrices
Random trees and branching processesGalton-Watson processes Multitype branching processes in random environment Local and scaling limits of large random trees, continuum random trees Brownian snake Branching random walks and Fisher-KPP equations
Stochastic processes and random fieldsCentral limit theorem and invariance principle for random processes Self similar random fields Stochastic geometry (GDR GeoSto ) Diffusions in Levy’s potential Stochastic models for population dynamics and neuron dynamics Stochastic PDE’s and regularity structures Reflected Brownian motion Harmonic analysis and Dunkl Processes Logarithmic Sobolev type inequalities and applications in probability theory Piecewise deterministic Markov processes (ANR PIECE (2013-2017))
Statistical mechanicsMetastability Diffusion of interacting Brownian particles Dimer models in statistical mechanics Stochastic models for population dynamics Percolation and first-passage percolation (ANR PPPP (2017-2021)) Interacting particles systems
Algebra Representations of Coxeter groups and Hecke algebras, basic sets and decomposition matrices Representations of Lie algebras and quantum groups, canonical and crystal bases Kazhdan-Lusztig theory and Kazhdan-Lusztig cells Reflection groups, braid groups, Hecke algebras, and categorical incarnations. Noncommutative algebra
Combinatorics Algebraic combinatoricsPreorder and associated graphs Additive number theory and generalizations Combinatorics of root systems Combinatorics of words Additive combinatorics and generalizations Enumerative combinatoricsEnumeration of walks in cones Enumeration of decorated planar maps Functional equations Analytic combinatorics
Ergodic theory, dynamical systems and ergodic geometry Simple and multiple ergodic averages Limit Theorems for dynamical systems Orbital functions and counting of closed geodesics in negative curvature Limit theorem for the geodesic flow in negative curvature Entropy and growth of volume of balls in negative curvature (GDR PLATON ) Combinatorial number theory
