The 123 theorem and its extensions

Noga Alon, Raphael Yuster

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)322-331
Number of pages10
JournalJournal of Combinatorial Theory - Series A
Issue number2
StatePublished - Nov 1995
Externally publishedYes

Bibliographical note

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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