Probability

Team Members

Permanent Members Non permanent Members
  • Julie Fournier (Ph.D student)
  • Alkéos Michail (Ph.D student)
  • Cambyse Pakzad (Ph.D student)

The team seminar, organized by Raphaël Lachièze-Rey and Eric Luçon is held approximately every two weeks. For more information, please refer to the seminar page.

A monthly workshop « Random Matrices and Graphs » MEGA, is organized by Camille Male, at « Institut Henri Poincaré ».

A workshop on Statistical Mechanics and Particle Systems, co-organized by Ellen Saada is held at IHP approximately every 6 weeks.

Probability research themes :

Team research interests are, in no particular order:

Interacting particle systems

Keywords : systems with « strong » or « local » interaction, exclusion processes, zero range processes, spin systems, hydrodynamic limits, coupling, attractivity, sandpile models,  random graphs, particles in random environment, propagation of epidemies, contact process, percolation.

Mean-field interacting particle systems, synchronization, Kuramoto model, neuronal models, diffusions on (random) graphs, propagation of chaos, measure valued processes, large deviations.

Stochastic calculus :

Keywords : stochastic analysis, Malliavin calculus, stochastic partial differential equations (SPDEs), central limit theorem, fractional Brownian motion, fractal analysis.

Stochastic geometry :

Keywords : stochastic geometry, random fields, limit theorems, Gaussian fields, shot-noise processes, long memory, point processes, Poisson processes, geometric functionals, boolean model, spatio-temporal models, random sets, random polytopes, level sets, Euler characteristic, topological properties of random excursions, regularity, autosimilarity, random tessellations, anisotropy, Stein method.

Functional inequalities :

Keywords : functional or geometric inequalities and applications in probability, optimal transport, large  deviations, concentration of measure, Markov processes.

Random matrices :

Keywords : free probability theory, Marçenko-Pastur Theorem, spectral analysis, random graphs, hypergraphs, GUE, GOE, determinantal processes, localization, Haar measure, semi-circle law, universality, integrable systems, Tracy-Widom law, Airy kernel, Beta ensembles.

Brownian motions in cones, Kac Moody algebras, loop groups and algebras, Brownian unitary or Hermitian sheets, Kirillov/Frenkel formula.

Collective projects :