Research output: Contribution to journal › Article › peer-review
Régularisation spectrale en théorie ergodique et théorie des probabilités. / Lifshits, Mikhail; Weber, Michel.
In: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, Vol. 324, No. 1, 01.01.1997, p. 99-103.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Régularisation spectrale en théorie ergodique et théorie des probabilités
AU - Lifshits, Mikhail
AU - Weber, Michel
PY - 1997/1/1
Y1 - 1997/1/1
N2 - We show that the idea of spectral regularization introduced by Talagrand in the study of covering numbers of averages of contractions in a Hilbert space H can be concentrated in one inequality which turns out to be a suitable tool for the study of other characteristics of the set of averages. This inequality generates an intrinsic Lipschitz embedding of the circle and yields many useful corollaries. We also easily deduce the original Talagrand estimate of covering numbers and provide better estimates for geometric subsequences of the averages. Using majorizing measuring technique, we prove a new criterion of the a.s. convergence of random sequences under suitable incremental conditions. We obtain as a corollary the classical theorem of Rademacher-Menshov on orthogonal series and the famous spectral criterion for the strong law of large numbers due to Gaposhkin.
AB - We show that the idea of spectral regularization introduced by Talagrand in the study of covering numbers of averages of contractions in a Hilbert space H can be concentrated in one inequality which turns out to be a suitable tool for the study of other characteristics of the set of averages. This inequality generates an intrinsic Lipschitz embedding of the circle and yields many useful corollaries. We also easily deduce the original Talagrand estimate of covering numbers and provide better estimates for geometric subsequences of the averages. Using majorizing measuring technique, we prove a new criterion of the a.s. convergence of random sequences under suitable incremental conditions. We obtain as a corollary the classical theorem of Rademacher-Menshov on orthogonal series and the famous spectral criterion for the strong law of large numbers due to Gaposhkin.
UR - http://www.scopus.com/inward/record.url?scp=0030640386&partnerID=8YFLogxK
M3 - статья
AN - SCOPUS:0030640386
VL - 324
SP - 99
EP - 103
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
SN - 1631-073X
IS - 1
ER -
ID: 43811621