Palindromic random trigonometric polynomials

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dc.creatorConrey, J. Brian
dc.creatorFarmer, David W.
dc.creatorImamoglu, Özlem
dc.date2008-12-09
dc.date.accessioned2026-07-07T12:10:52Z
dc.date.available2026-07-07T12:10:52Z
dc.descriptionWe show that if a real trigonometric polynomial has few real roots, then the trigonometric polynomial obtained by writing the coefficients in reverse order must have many real roots. This is used to show that a class of random trigonometric polynomials has, on average, many real roots. In the case that the coefficients of a real trigonometric polynomial are independently and identically distributed, but with no other assumptions on the distribution, the expected fraction of real zeros is at least one-half. This result is best possible.
dc.description5 pages. To appear in PAMS
dc.identifierhttps://arxiv.org/abs/0812.1752
dc.identifierhttp://arxiv.org/abs/0812.1752
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210056
dc.subjectProbability
dc.subjectComplex Variables
dc.subject60G99; 42A05; 30C15
dc.titlePalindromic random trigonometric polynomials
dc.typetext

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