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- W3011008510 abstract "Notons $lambda_{1}(A),ldots ,lambda_{n}(A)$ les valeurs propres d’une matrice $A$ de taille $ntimes n$. Soit $Z_{n}$ une matrice $ntimes n$ choisie aléatoirement et uniformément dans l’équivalent matriciel de la boule unité de l’ensemble classique $ell_{p}^{n}$, défini comme l’ensemble des matrices $ntimes n$ auto-adjointes satisfaisant $sum_{k=1}^{n}|lambda_{k}(A)|^{p} leq 1$. Nous prouvons un principe de grandes déviations pour la mesure spectrale aléatoire de la matrice $n^{1/p}Z_{n}$. Comme conséquence, nous obtenons que la mesure spectrale de $n^{1/p}Z_{n}$ converge faiblement presque sûrement vers une mesure déterministe limite décrite par la loi d’Ullman lorsque $n$ tend vers l’infini. Nous présentons également les résultats correspondants pour les matrices aléatoires dans les classes de trace de Schatten, où les valeurs propres sont remplacées par les valeurs singulières." @default.
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- W3011008510 date "2020-05-01" @default.
- W3011008510 modified "2023-10-18" @default.
- W3011008510 title "Sanov-type large deviations in Schatten classes" @default.
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- W3011008510 doi "https://doi.org/10.1214/19-aihp989" @default.
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