The 123 theorem and its extensions

Noga Alon; Raphael Yuster

doi:10.1016/0097-3165(95)90071-3

The 123 theorem and its extensions

Noga Alon, Raphael Yuster

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

It is shown that for every b > a > 0 and for every two independent identically distributed real random variables X and Y, Prob[|X Y|≤b] (2{top left corner} b a {top right corner} 1) Prob[|X Y|≤a]. This is tight for all admissible pairs a, b. Higher dimensional extensions are also considered.

Original language	English (US)
Pages (from-to)	322-331
Number of pages	10
Journal	Journal of Combinatorial Theory, Series A
Volume	72
Issue number	2
DOIs	https://doi.org/10.1016/0097-3165(95)90071-3
State	Published - Nov 1995
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/0097-3165(95)90071-3

Cite this

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title = "The 123 theorem and its extensions",

abstract = "It is shown that for every b > a > 0 and for every two independent identically distributed real random variables X and Y, Prob[|X Y|≤b] (2\{top left corner\} b a \{top right corner\} 1) Prob[|X Y|≤a]. This is tight for all admissible pairs a, b. Higher dimensional extensions are also considered.",

author = "Noga Alon and Raphael Yuster",

note = "Funding Information: * Research supported in part by a United States Israel BSF Grant.",

year = "1995",

month = nov,

doi = "10.1016/0097-3165(95)90071-3",

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journal = "Journal of Combinatorial Theory, Series A",

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AU - Alon, Noga

AU - Yuster, Raphael

N1 - Funding Information: * Research supported in part by a United States Israel BSF Grant.

PY - 1995/11

Y1 - 1995/11

N2 - It is shown that for every b > a > 0 and for every two independent identically distributed real random variables X and Y, Prob[|X Y|≤b] (2{top left corner} b a {top right corner} 1) Prob[|X Y|≤a]. This is tight for all admissible pairs a, b. Higher dimensional extensions are also considered.

AB - It is shown that for every b > a > 0 and for every two independent identically distributed real random variables X and Y, Prob[|X Y|≤b] (2{top left corner} b a {top right corner} 1) Prob[|X Y|≤a]. This is tight for all admissible pairs a, b. Higher dimensional extensions are also considered.

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U2 - 10.1016/0097-3165(95)90071-3

DO - 10.1016/0097-3165(95)90071-3

M3 - Article

AN - SCOPUS:33750616069

SN - 0097-3165

VL - 72

SP - 322

EP - 331

JO - Journal of Combinatorial Theory, Series A

JF - Journal of Combinatorial Theory, Series A

IS - 2

ER -

The 123 theorem and its extensions

Abstract

All Science Journal Classification (ASJC) codes

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