A note on the quicksort asymptotics1. Issue 4 (19th November 2013)

• Record Type: Journal Article
• Authors: Fuchs, Michael
• Is Part Of: Random structures & algorithms. Volume 46:Issue 4(2015)
• Page Start: 677
• Page End: 687
• Publication Date: 2013-11-19
• Subjects: Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20524
• Languages: English
• ISSNs: 1042-9832

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>In a recent paper, Bindjeme and Fill obtained a surprisingly easy exact formula for the <italic>L</italic>₂‐distance of the (normalized) number of comparisons of Quicksort under the uniform model to its limit. Shortly afterwards, Neininger proved a central limit theorem for the error. As a consequence, he obtained the asymptotics of the <italic>L</italic>₃‐distance. In this short note, we use the moment transfer approach to re‐prove Neininger's result. As a consequence, we obtain the asymptotics of the <italic>L</italic>_p‐distance for all <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgjmx7rz3w" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley::media:rsa20524:rsa20524-math-0003" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>Copyright © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 677–687, 2015</p> </abstract>