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Dive into the research topics where Sandrine Péché is active.

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Featured researches published by Sandrine Péché.


Annals of Probability | 2005

Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices

Jinho Baik; Gérard Ben Arous; Sandrine Péché

AbstractWe compute the limiting distributions of the largest eigenvalue of a complex Gaussian samplecovariance matrix when both the number of samples and the number of variables in each samplebecome large. When all but finitely many, say r, eigenvalues of the covariance matrix arethe same, the dependence of the limiting distribution of the largest eigenvalue of the samplecovariance matrix on those distinguished r eigenvalues of the covariance matrix is completelycharacterized in terms of an infinite sequence of new distribution functions that generalizethe Tracy-Widom distributions of the random matrix theory. Especially a phase transitionphenomena is observed. Our results also apply to a last passage percolation model and aqueuing model. 1 Introduction Consider M independent, identically distributed samples y 1 ,...,~y M , all of which are N ×1 columnvectors. We further assume that the sample vectors ~y k are Gaussian with mean µ and covarianceΣ, where Σ is a fixed N ×N positive matrix; the density of a sample ~y isp(~y) =1(2π)


Probability Theory and Related Fields | 2011

Eigenvectors of Some Large Sample Covariance Matrices Ensembles

Olivier Ledoit; Sandrine Péché

We consider sample covariance matrices constructed from real or complex i.i.d. variates with finite 12th moment. We assume that the population covariance matrix is positive definite and its spectral measure almost surely converges to some limiting probability distribution as the number of variables and the number of observations go to infinity together, with their ratio converging to a finite positive limit. We quantify the relationship between sample and population eigenvectors, by studying the asymptotics of a broad family of functionals that generalizes the Stieltjes transform of the spectral measure. This is then used to compute the asymptotically optimal bias correction for sample eigenvalues, paving the way for a new generation of improved estimators of the covariance matrix and its inverse.


Communications on Pure and Applied Mathematics | 2010

Limit process of stationary TASEP near the characteristic line

Jinho Baik; Patrik L. Ferrari; Sandrine Péché

The totally asymmetric simple exclusion process (TASEP) on\input amssym


Journal of Statistical Physics | 2008

Airy kernel with two sets of parameters in directed percolation and random matrix theory.

Alexei Borodin; Sandrine Péché

{\Bbb Z}


Annales De L Institut Henri Poincare-probabilites Et Statistiques | 2009

Poisson convergence for the largest eigenvalues of heavy tailed random matrices

Antonio Auffinger; Gérard Ben Arous; Sandrine Péché

with the Bernoulli-ρ measure as an initial condition, 0 < ρ < 1, is stationary. It is known that along the characteristic line, the current fluctuates at an order of t1/3. The limiting distribution has also been obtained explicitly. In this paper we determine the limiting multipoint distribution of the current fluctuations moving away from the characteristics by the order t2/3. The main tool is the analysis of a related directed last percolation model. We also discuss the process limit in tandem queues in equilibrium.


Annales De L Institut Henri Poincare-probabilites Et Statistiques | 2012

Universality of slow decorrelation in KPZ growth

Ivan Corwin; Patrik L. Ferrari; Sandrine Péché

We introduce a generalization of the extended Airy kernel with two sets of real parameters. We show that this kernel arises in the edge scaling limit of correlation kernels of determinantal processes related to a directed percolation model and to an ensemble of random matrices.


Journal of Statistical Physics | 2010

Limit Processes for TASEP with Shocks and Rarefaction Fans

Ivan Corwin; Patrik L. Ferrari; Sandrine Péché

On etudie la loi des plus grandes valeurs propres de matrices aleatoires symetriques reelles et de covariance empirique quand les coefficients des matrices sont a queue lourde. On etend le resultat obtenu par Soshnikov dans (Electron. Commun. Probab. 9 (2004) 82-91) et on montre que le comportement asymptotique des plus grandes valeurs propres est determine par les plus grandes entrees de la matrice.


arXiv: Mathematical Physics | 2014

Convergence of the Two-Point Function of the Stationary TASEP

Jinho Baik; Patrik L. Ferrari; Sandrine Péché

There has been much success in describing the limiting spatial fluctuations of growth models in the Kardar-Parisi-Zhang (KPZ) universality class. A proper rescaling of time should introduce a non-trivial temporal dimension to these limiting fluctuations. In one-dimension, the KPZ class has the dynamical scaling exponent


Annales De L Institut Henri Poincare-probabilites Et Statistiques | 2014

Localization and delocalization for heavy tailed band matrices

Florent Benaych-Georges; Sandrine Péché

z=3/2


Journal of Statistical Physics | 2014

A Note on the Second Order Universality at the Edge of Coulomb Gases on the Plane

Djalil Chafaï; Sandrine Péché

, that means one should find a universal space-time limiting process under the scaling of time as

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Jinho Baik

University of Michigan

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Alexei Borodin

Massachusetts Institute of Technology

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Djalil Chafaï

Paris Dauphine University

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