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Small deviations of sums of random v...

Rutgers The State University of New Jersey - New Brunswick.

Small deviations of sums of random variables.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Small deviations of sums of random variables./
Author:	Garnett, Brian.
Description:	1 online resource (59 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-04(E), Section: B.
Contained By:	Dissertation Abstracts International78-04B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369349894

Small deviations of sums of random variables.
Garnett, Brian.

Small deviations of sums of random variables. - 1 online resource (59 pages)

Source: Dissertation Abstracts International, Volume: 78-04(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

In this thesis, we study the probability of a small deviation from the mean of a sum of independent or semi-independent random variables. In contrast with the rich history of large deviation inequalities, small deviations have only recently gained attention, and we make contributions to several problems on this topic.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369349894Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Small deviations of sums of random variables.
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008 190606s2016 xx obm 000 0 eng d
020 $a 9781369349894
035 $a (MiAaPQ)AAI10291807
035 $a (MiAaPQ)rutgersnb:7260
035 $a AAI10291807
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Garnett, Brian. $3 1180782
245 1 0 $a Small deviations of sums of random variables.
264 0 $c 2016
300 $a 1 online resource (59 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-04(E), Section: B.
500 $a Adviser: Swastik Kopparty.
502 $a Thesis (Ph.D.) $c Rutgers The State University of New Jersey - New Brunswick $d 2016.
504 $a Includes bibliographical references
520 $a In this thesis, we study the probability of a small deviation from the mean of a sum of independent or semi-independent random variables. In contrast with the rich history of large deviation inequalities, small deviations have only recently gained attention, and we make contributions to several problems on this topic.
520 $a Perhaps the most significant result in this field was an inequality proved by Feige. Let X1, . . . , Xn be nonnegative independent random variables, with E[ Xi] ≤ 1 ∀i, and let X = sum(n/i=1) X i. Then for any n, Pr[X 0, for some alpha ≥ 1/13. This bound was later improved to 1/8 by He, Zhang, and Zhang. Building off their work, we improve the bound to approximately .14. The conjectured true bound is 1/e &sime; .368, so there is still (possibly) quite a gap left to fill.
520 $a We also consider whether or not such small deviation inequalities hold for k-wise independent random variables. We show that for some classes of random variables, 4- wise independence is sufficient for a constant lower bound of alpha = 1/6, which we show to be tight. Furthermore, we present counterexamples showing that 3-wise independence is insufficient for a positive constant lower bound.
520 $a For sums of Bernoulli random variables, we can let alpha = 1/ e. We also show that k-wise independence can bring us arbitrarily close to that bound for large enough k.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Theoretical mathematics. $3 1180455
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0642
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Rutgers The State University of New Jersey - New Brunswick. $b Graduate School - New Brunswick. $3 845606
773 0 $t Dissertation Abstracts International $g 78-04B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10291807 $z click for full text (PQDT)

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