Exposés
Les rencontres seront composées de deux minicours, de conférences
de 45 minutes, ainsi que de sessions posters.
Minicours
 Massimiliano
GUBINELLI (CEREMADE, Université Paris Dauphine).
Singular Stochastic PDEs and paracontrolled distributions.
 Bálint TÓTH (School of Mathematics,
University of Bristol, England; Institute of Mathematics, TU,
Budapest, Hungary).
Scaling limits for random walks and
diffusions with long memory  resolvent methods.
Conférences

MohamedAmine ASSELAH
(LAMA, Université ParisEst).

Christophe BAHADORAN
(Université Blaise Pascal, Clermont Ferrand).

Cédric BERNARDIN
(Laboratoire Dieudonné, Université de Nice SophiaAntipolis).

Thierry BODINEAU,
(CNRS, CMAP, École Polytechnique).

Ivan CORWIN
(Clay Mathematics Institute, Columbia
University, Institute Henri Poincare, Massachusetts Institute of
Technology, Cambridge, USA).

Alexandre GAUDILLIERE
(CNRS, LATP, Université d'Aix Marseille)

Régine MARCHAND
(Institut Elie Cartan, Université de Lorraine, Nancy).

Stefano OLLA
(CEREMADE, Université Paris Dauphine).

Mathew PENROSE
(University of Bath, England).

Christophe SABOT
(Institut Camille Jordan, Université Claude Bernard, Lyon).

Renato Soares DOS SANTOS
(Institut Camille Jordan, Université Claude Bernard, Lyon).
Posters
 Kevin KUOCH (Université Paris Descartes).
 Achref MAJID (Faculté des sciences de Tunis El Manar).
 Arnaud ROUSSELLE (Université de Rouen).
Liste des participants
À
télécharger
ici.
Résumés

MohamedAmine ASSELAH
(LAMA, Université ParisEst).
On two deposition models.
I discuss properties of a two models of stochastic deposition:
ballistic and diffusive limited deposition.

Christophe BAHADORAN,
(Université Blaise Pascal, Clermont Ferrand).
Phase transition for disordered TASEP.
We prove that the currentdensity relation of TASEP with site disorder exhibits a plateau around density
1/2 for sufficiently dilute disorder. This result was first conjectured by Tripathy and Barma (1998). The
difficulty is that invariant measures are unknown in the case of site disorder contrary to particle disorder,
where the existence of a linear portion on the current can be
established by explicit computation. Our
proof uses a renormalization scheme and last passage percolation.
This is a joint work with T. Bodineau.

Cédric
BERNARDIN(Université de Nice
SophiaAntipolis).
3/4 fractional superdiffusion of energy in a harmonic chain with bulk noises.
We consider a harmonic chain perturbed by an energy conserving noise and show
that after a spacetime rescaling the energyenergy correlation function is
given by the solution of a skewfractional heat equation with exponent 3/4.

Thierry BODINEAU
(CNRS, CMAP, École Polytechnique).
Tagged particle in a deterministic dynamics of hard spheres.
We consider a tagged particle in a diluted gas of hard
spheres. Starting from the hamiltonian dynamics of particles in the
BoltzmannGrad limit, we will show that the tagged particle follows a
Brownian motion after an appropriate rescaling. We use the linear
Boltzmann equation as an intermediate level of description for one
tagged particle in a gas close to global equilibrium.

Ivan
CORWIN (Clay Mathematics Institute, Columbia
University, Institute Henri Poincare, Massachusetts Institute of
Technology, Cambridge, USA).
Macdonald processes, quantum integrable systems and the KPZ universality class.
A large class of one dimensional systems are predicted to share the
same universal longtime/largescale behaviors. By studying certain
integrable models within this KardarParisiZhang (KPZ) universality
class we access what should be universal statistics and phenomena. The
purpose of this talk is to give an introductory overview of how
representation theory and integrable systems can be harnessed in the
form of the theory of Macdonald processes and quantum integrable
systems to discover and analyze a variety of probabilistic models
(such as directed polymers, interacting particle systems, growth
processes, random matrices, and tilings).

Alexandre GAUDILLIERE
(CNRS, LATP, Université d'Aix Marseille)
Pyramidal algorithms for general graphs or metastability
without asymptotic.
We propose some adaptation for general graphs of usual pyramidal algorithms of signal processing to
bridge between standard techniques of multiscale analysis and usual approaches to metastability. This
makes possible to deal wtih metastable dynamics outside any asymptotic regime.
This is work in progress with Luca Avena, Fabienne Castel and Clothilde Melot.
 Massimiliano
GUBINELLI (CEREMADE, Université Paris Dauphine).
Singular Stochastic PDEs and paracontrolled distributions.
These two lectures will be devoted to the introduction of an analytic
framework for the formulation of nonlinear evolution problems
perturbed by singular noise sources which can arise as scaling limits
of certain microscopic evolutions. The parabolic anderson model, the
KardarParisiZhang equation and the stochastic quantization equation
are examples of such systems. Solving (or even giving a meaning to)
these equations require a detailed understanding of the propagation of
the stochastic perturbations via the nonlinear evolution. I will
explain how ideas and tools from harmonic analysis can be useful in
this analysis and in the related problem of studying the convergence
of the microscopic models to their scaling limits.

Régine MARCHAND
(Institut Elie Cartan, Université de Lorraine, Nancy).
Boolean percolation in high dimension.
In the boolean percolation model in $\mathbb{R}^d$, random balls are thrown in
the following manner:
 centers are chosen accordingly to a homogeneous Poisson point process with intensity $\lambda$ in $\mathbb{R}^d$,
 radii are iid random variables with common distribution $\nu$, also independent from the centers.
We say that percolation occurs if there exists an infinite connected component of balls: there is a
critical parameter $\lambda_c(\nu)$ such that if $\lambda <\lambda_c(\nu)$, there is a.s. no percolation,
while if $\lambda>\lambda_c(\nu)$, percolation occurs with positive probability.
We investigate here the distribution of radius $\nu$ which minimizes the critical parameter $\lambda_c(\nu)$.
In particular, by studying the asymptotic of this critical parameter $\lambda_c(\nu)$ when $\nu$
only charges two distinct radii, we disprove the conjecture that constant radii should be optimal.
 Stefano OLLA
(CEREMADE, Université Paris Dauphine).
A Wigner distribution approach to hydrodynamic limits: diffusion and superdiffusion of energy.

Mathew PENROSE
(University of Bath, England).
Random parking and rubber elasticity.
Renyi's random parking process on a domain D in dspace is a point
process with hardcore and noemptyspace properties that are
desirable for modelling materials such as rubber. It is obtained
as follows: particles arrive sequentially at uniform random
locations in D, and are rejected if they violate the hardcore
constraint, until the accepted particles saturate D.
We describe how any realvalued functional on this point process, provided
it enjoys certain subadditivity properties, satisfies an averaging
property in the thermodynamic limit. Consequently in this limit,
one has a convergence of macoroscopicallydefined energy
functionals for deformations of the point process, to a
homogenized limiting energy functional. We may also apply the
results to derive laws of large numbers for classical optimization
problems such as travelling salesman on the parking point process.
This is joint work with Antoine Gloria.

Christophe
SABOT
(Institut Camille Jordan, Université Claude Bernard, Lyon).
The Vertex Reinforced Jump Process and the inversion of the generalized RayKnight identity.
The vertex reinforced jump process (VRJP) is a selfinteracting process closely related to the Edge Re
inforced Random Walk. The generalized RayKnight identity relates the local time of a Markov jump
process to the associated Gaussian free field. After a review of recent results on these processes I will
explain how the RayKnight identity can be "inverted" using ideas coming from the VRJP.

Renato Soares Dos SANTOS
(Institut Camille Jordan, Université Claude Bernard, Lyon).
Random walk on random
walks.
We study a random walk in a dynamical random environment given by a
Poissonian system of independent random walks in equilibrium, for
which we prove a law of large numbers and a central limit theorem in a
large density regime.

Bálint
TÓTH
(School of Mathematics, University of Bristol, England; Institute of Mathematics, TU,
Budapest, Hungary).
Scaling limits for random walks and diffusions with long memory 
resolvent methods.
I will survey recent results on diffusivity bounds and central limit
theorem for random walks and diffusions with pathwise selfinteraction and
for random walks and diffusions in a particular class of random
environment. The results rely on analysis of the infinitesimal generator
and resolvent of the semigroup of Markov processes related to the
walks/diffusions in question. The lectures will be selfcontained, I will
survey classical and new results related to additive functionals of ergodic
Markov processes.