Double roots of random polynomials with integer coefficients

Ohad N. Feldheim, Arnab Sen

Research output: Contribution to journalArticlepeer-review

Abstract

We consider random polynomials whose coefficients are independent and identically distributed on the integers. We prove that if the coefficient distribution has bounded support and its probability to take any particular value is at most 1 2, then the probability of the polynomial to have a double root is dominated by the probability that either 0, 1, or -1 is a double root up to an error of o(n-2). We also show that if the support of the coefficients’ distribution excludes 0, then the double root probability is O(n-2). Our result generalizes a similar result of Peled, Sen and Zeitouni [13] for Littlewood polynomials.

Original languageEnglish (US)
Article number10
JournalElectronic Journal of Probability
Volume22
DOIs
StatePublished - 2017

Bibliographical note

Funding Information:
Supported in part by the IMA with funds provided by the NSF. Supported in part by NSF grant DMS-1406247.

Keywords

  • Algebraic numbers
  • Anti-concentration
  • Double roots
  • Random polynomials

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