On algebraic polynomials with random coefficients
Author:
K. Farahmand
Journal:
Proc. Amer. Math. Soc. 129 (2001), 27632769
MSC (2000):
Primary 60H99; Secondary 60G15
Published electronically:
March 15, 2001
MathSciNet review:
1838800
Fulltext PDF Free Access
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Abstract: The expected number of real zeros and maxima of the curve representing algebraic polynomial of the form where , are independent standard normal random variables, are known. In this paper we provide the asymptotic value for the expected number of maxima which occur below a given level. We also show that most of the zero crossings of the curve representing the polynomial are perpendicular to the axis. The results show a significant difference in mathematical behaviour between our polynomial and the random algebraic polynomial of the form which was previously the most studied.
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Additional Information
K. Farahmand
Affiliation:
Department of Mathematics, University of Ulster, Jordanstown, Co. Antrim BT37 0QB, United Kingdom
Email:
k.farahmand@ulst.ac.uk
DOI:
http://dx.doi.org/10.1090/S0002993901058361
PII:
S 00029939(01)058361
Keywords:
Number of real roots,
real zeros,
number of maxima,
random algebraic polynomials,
KacRice formula
Received by editor(s):
September 1, 1999
Received by editor(s) in revised form:
January 26, 2000
Published electronically:
March 15, 2001
Communicated by:
Claudia M. Neuhauser
Article copyright:
© Copyright 2001
American Mathematical Society
