Anti-concentration for polynomials of independent random variables

Raghu Meka, Oanh Nguyen, Van Vu

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

We prove anti-concentration results for polynomials of independent random variables with arbitrary degree. Our results extend the classical Littlewood-Offord result for linear polynomials, and improve several earlier estimates. We discuss applications in two different areas. In complexity theory, we prove nearoptimal lower bounds for computing the PARITY function, addressing a challenge in complexity theory posed by Razborov and Viola, and also address a problem concerning the OR function. In random graph theory, we derive a general anti-concentration result on the number of copies of a fixed graph in a random graph.

Original languageEnglish (US)
Article number11
JournalTheory of Computing
Volume12
DOIs
StatePublished - 2016

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computational Theory and Mathematics

Keywords

  • Anti-concentration
  • Complexity theory
  • Parity
  • Random graphs
  • Random polynomials

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