Minima of sequences of Gaussian random variables

Yehoram Gordon, Alexander Litvak, Carsten Schütt, Elisabeth Werner

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


For a given sequence of real numbers a1,..., an we denote the k-th smallest one by k-min1≤i≤nai. We show that there exist two absolute positive constants c and C such that for every sequence of positive real numbers x1,..., xn and every k ≤ n one has c max1≤j≤k k+1-j/∑i=jn 1/xi ≤ E k- min1≤i≤n xigi ≤ C ln(k + 1) max1≤j≤k k+1-j/∑i=jn 1/xi, where gi ∈ N(0, 1), i = 1,..., n, are independent Gaussian random variables. Moreover, if k = 1 then the left hand side estimate does not require independence of the gis. Similar estimates hold for E k- min1≤i≤n xi gi p as well.

Original languageEnglish (US)
Pages (from-to)445-448
Number of pages4
JournalComptes Rendus Mathematique
Issue number6
StatePublished - Mar 15 2005
Externally publishedYes

Bibliographical note

Funding Information:
E-mail addresses: (Y. Gordon), (A. Litvak), (C. Schütt), (E. Werner). 1 This author is partially supported by the Fund for the Promotion of Research at the Technion. 2 This author is partially supported by FP6 Marie Curie Actions, MRTN-CT-2004-511953, PHD. 3 This author is partially supported by a NSF Grant, by a Nato Collaborative Linkage Grant and by a NSF Advance Opportunity Grant.


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