Non-abelian Littlewood-Offord inequalities

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• 作者：Pham H. Tiep^a ; ¹ ; ³ ; ^{tiep@math.arizona.edu" class="auth_mail" title="E-mail the corresponding author} ; Van H. Vu^b ; ² ; ³ ; ^{van.vu@yale.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 05D40 ; 20C33 ; secondary ; 60B15 ; 60C05 ; 60G50
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：22 October 2016
• 年：2016
• 卷：302
• 期：Complete
• 页码：1233-1250
• 全文大小：380 K

文摘

In 1943, Littlewood and Offord proved the first anti-concentration result for sums of independent random variables. Their result has since then been strengthened and generalized by generations of researchers, with applications in several areas of mathematics.

In this paper, we present the first non-abelian analogue of the Littlewood–Offord result, a sharp anti-concentration inequality for products of independent random variables.