A tail bound for read‐k families of functions1. Issue 1 (6th March 2014)

• Record Type: Journal Article
• Authors: Gavinsky, Dmitry; Lovett, Shachar; Saks, Michael; Srinivasan, Srikanth
• Is Part Of: Random structures & algorithms. Volume 47:Issue 1(2015)
• Page Start: 99
• Page End: 108
• Publication Date: 2014-03-06
• Subjects: Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20532
• Languages: English
• ISSNs: 1042-9832

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>We prove a Chernoff‐like large deviation bound on the sum of non‐independent random variables that have the following dependence structure. The variables <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj14cqm21q" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:10429832:media:rsa20532:rsa20532-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Y</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>, </mml:mo><mml:mo>…</mml:mo><mml:mo>, </mml:mo><mml:msub><mml:mi>Y</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula> are arbitrary [0, 1]‐valued functions of independent random variables <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj14cqm39n" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:10429832:media:rsa20532:rsa20532-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>, </mml:mo><mml:mo>…</mml:mo><mml:mo>, </mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>m</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>, modulo a restriction that every <italic>X</italic><sub><italic>i</italic></sub> influences at most <italic>k</italic> of the variables <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj14cqm3b6" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:10429832:media:rsa20532:rsa20532-math-0003" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Y</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>, </mml:mo><mml:mo>…</mml:mo><mml:mo>, </mml:mo><mml:msub><mml:mi>Y</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula>. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 99–108, 2015</p> </abstract>