Pour une suite des nombres réels, on note le k-ième plus petit membre par . On démontre qu'il existe deux constants positives c et C telles que pour toute suite des nombres réels et pour tout , on ait
For a given sequence of real numbers we denote the k-th smallest one by . We show that there exist two absolute positive constants c and C such that for every sequence of positive real numbers and every one has
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@article{CRMATH_2005__340_6_445_0, author = {Gordon, Yehoram and Litvak, Alexander and Sch\"utt, Carsten and Werner, Elisabeth}, title = {Minima of sequences of {Gaussian} random variables}, journal = {Comptes Rendus. Math\'ematique}, pages = {445--448}, publisher = {Elsevier}, volume = {340}, number = {6}, year = {2005}, doi = {10.1016/j.crma.2005.02.003}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.02.003/} }
TY - JOUR AU - Gordon, Yehoram AU - Litvak, Alexander AU - Schütt, Carsten AU - Werner, Elisabeth TI - Minima of sequences of Gaussian random variables JO - Comptes Rendus. Mathématique PY - 2005 SP - 445 EP - 448 VL - 340 IS - 6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.02.003/ DO - 10.1016/j.crma.2005.02.003 LA - en ID - CRMATH_2005__340_6_445_0 ER -
%0 Journal Article %A Gordon, Yehoram %A Litvak, Alexander %A Schütt, Carsten %A Werner, Elisabeth %T Minima of sequences of Gaussian random variables %J Comptes Rendus. Mathématique %D 2005 %P 445-448 %V 340 %N 6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.02.003/ %R 10.1016/j.crma.2005.02.003 %G en %F CRMATH_2005__340_6_445_0
Gordon, Yehoram; Litvak, Alexander; Schütt, Carsten; Werner, Elisabeth. Minima of sequences of Gaussian random variables. Comptes Rendus. Mathématique, Tome 340 (2005) no. 6, pp. 445-448. doi : 10.1016/j.crma.2005.02.003. http://archive.numdam.org/articles/10.1016/j.crma.2005.02.003/
[1] Orlicz norms of sequences of random variables, Ann. Probab., Volume 30 (2002), pp. 1833-1853
[2] S. Mallat, O. Zeitouni, Optimality of the Karhunen–Loeve basis in nonlinear reconstruction, preprint, http://www.ee.technion.ac.il/~zeitouni/openprob.html
[3] O. Zeitouni, private communication
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