On random algebraic polynomials

Author:
K. Farahmand

Journal:
Proc. Amer. Math. Soc. **127** (1999), 3339-3344

MSC (1991):
Primary 60H99; Secondary 42Bxx

DOI:
https://doi.org/10.1090/S0002-9939-99-04912-6

Published electronically:
May 6, 1999

MathSciNet review:
1610956

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper provides asymptotic estimates for the expected number of real zeros and -level crossings of a random algebraic polynomial of the form , where are independent standard normal random variables and is a constant independent of . It is shown that these asymptotic estimates are much greater than those for algebraic polynomials of the form .

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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:
https://doi.org/10.1090/S0002-9939-99-04912-6

Keywords:
Number of real roots,
real zeros,
random algebraic polynomials,
random trigonometric polynomials,
Kac-Rice formula

Received by editor(s):
July 9, 1997

Received by editor(s) in revised form:
December 17, 1997, and February 5, 1998

Published electronically:
May 6, 1999

Communicated by:
Stanley Sawyer

Article copyright:
© Copyright 1999
American Mathematical Society