THE EXPECTED NUMBER OF LOCAL MAXIMA OF A RANDOM ALGEBRAIC POLYNOMIAL

Authors
FARAHMAND K HANNIGAN P
Citation
K. Farahmand et P. Hannigan, THE EXPECTED NUMBER OF LOCAL MAXIMA OF A RANDOM ALGEBRAIC POLYNOMIAL, Journal of theoretical probability, 10(4), 1997, pp. 991-1002
Citations number
10
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Journal of theoretical probability → ACNP
ISSN journal
08949840
Volume
10
Issue
4
Year of publication
1997
Pages
991 - 1002
Database
ISI
SICI code
0894-9840(1997)10:4<991:TENOLM>2.0.ZU;2-P
Abstract
In this work we obtain an asymptotic estimate for the expected number of maxima of the random algebraic polynomial a(0) + a(1) + a(2)x(2) +. ..+ a(n-1)x(n-1), where a(j) (j = 0, 1,...,n-1) are independent, norma lly distributed random variables with mean mu and variance one. It is shown that for nonzero mu, the expected number of maxima is asymptotic to ((root 3 + 1)/4 pi) log n, when n is large.