Open AccessConcentration for independent random variables with heavy tails
Author(s) -
Franck Barthe,
Patrick Cattiaux,
Cyril Roberto
Publication year - 2005
Publication title -
applied mathematics research express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.763
H-Index - 20
eISSN - 1687-1200
pISSN - 1687-1197
DOI - 10.1155/amrx.2005.39
Subject(s) - random variable , mathematics , sequence (biology) , integrable system , variables , inequality , combinatorics , statistical physics , discrete mathematics , statistics , pure mathematics , physics , mathematical analysis , biology , genetics
If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish concentration inequalities for finite sequences of $n$ independent copies, with good dependence in $n$.
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