Published on *IHP | Institut Henri Poincaré | CNRS | UPMC * (http://ihp.fr)

**The Prize-winners** 2014-2015

for : "Maximum of a log-correlated Gaussian field". Read the article

Abstract

We study the maximum of a Gaussian field on [0,1]d(d≥1) whose correlations decay logarithmically with the distance. Kahane (Ann. Sci. Math. Québec 9 (1985) 105–150) introduced this model to construct mathematically the Gaussian multiplicative chaos in the subcritical case. Duplantier, Rhodes, Sheffield and Vargas (Critical Gaussian multiplicative chaos: Convergence of the derivative martingale (2012) Preprint, Renormalization of critical Gaussian multiplicative chaos and KPZ formula (2012) Preprint) extended Kahane’s construction to the critical case and established the KPZ formula at criticality. Moreover, they made in (Critical Gaussian multiplicative chaos: Convergence of the derivative martingale (2012) Preprint) several conjectures on the supercritical case and on the maximum of this Gaussian field. In this paper we resolve Conjecture 12 in (Critical Gaussian multiplicative chaos: Convergence of the derivative martingale (2012) Preprint): we establish the convergence in law of the maximum and show that the limit law is the Gumbel distribution convoluted by the limit of the derivative martingale.

for : "New insights into Approximate bayesian Computation". Read the article

Abstract

Approximate Bayesian Computation (ABC for short) is a family of computational techniques which offer an almost automated solution in situations where evaluation of the posterior likelihood is computationally prohibitive, or whenever suitable likelihoods are not available. In the present paper, we analyze the procedure from the point of view of k-nearest neighbor theory and explore the statistical properties of its outputs. We discuss in particular some asymptotic features of the genuine conditional density estimate associated with ABC, which is an interesting hybrid between a k-nearest neighbor and a kernel method.

**The Prize-winners 2012-2013**

for : "Universality for certain Hermitian Wigner matrices under weak moment conditions". Read the article

for "Superdiffusivity for Brownian Motion in a Poissonian potential with long range correlation I & II ". Read the articles : part I, part II

**The Prize-winners **2011

for : "Giant vacant component left by a random walk in a random d-regular graph". Read article here.

**The Prize-winners **2010

for : "Behavior near the extinction time in self-similar fragmentations I : The stable case". Read article here.

**The Prize-winners **2009

for "Anomalous heat-kernel decay for random walk among bounded random conductances." Read article here.

for "An asymptotic result for Brownian polymers". Read article here.

*Last updated 06/04/2016*