Statut  Confirmé 
Série  IPHTPHM 
Domaines  mathph 
Date  Lundi 27 Novembre 2017 
Heure  11:00 
Institut  IPHT 
Salle  Salle Claude Itzykson, Bât. 774 
Nom de l'orateur  Aurélien Grabsch 
Prenom de l'orateur  
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Titre  Truncated linear statistics of eigenvalues 
Résumé  Since the pioneer work of Wigner, random matrix theory have been applied to many fields in physics. Invariant ensembles have played a prominent role in physical applications, when eigenvalues and eigenvectors are uncorrelated. Many important physical observables take the form of linear statistics of eigenvalues $\{\lambda_i\}_{i=1,\ldots,N}$, i.e. $L = \sum_{i=1}^N f(\lambda_i)$, where $N$ is the total number of eigenvalues and $f$ is any given function depending on the physical situation under consideration. We have recently introduced a new type of problem: motivated by the analysis of the statistical physics of fluctuating onedimensional interfaces, we have studied the distribution of \textit{truncated} linear statistics $\tilde{L}=\sum_{i=1}^K f(\lambda_i)$, where the summation is restricted to number $K < N$ of the eigenvalues. In this talk, I will analyse two cases: first the case where the linear statistics is restricted to the largest (or smallest) $K$ eigenvalues. Then, I will discuss the case where any eigenvalue can contribute to the truncated linear statistics, without restriction on the ordering. I will show that, in a certain regime, this last problem can be mapped onto a system of noninteracting fermions which can have either positive or negative temperature. \\ \\ Refs: \\  Truncated linear statistics associated with the top eigenvalues of random matrices. Aurélien Grabsch, Satya N. Majumdar and Christophe Texier. J. Stat. Phys. 167(2), 234259 (2017) \\  Truncated linear statistics associated with the eigenvalues of random matrices II. Partial sums over proper time delays for chaotic quantum dots. Aurélien Grabsch, Satya N. Majumdar and Christophe Texier. J. Stat. Phys. 167(2) 14521488 (2017) 
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