IJPAM: Volume 97, No. 1 (2014)

EXPECTED NUMBER OF REAL ZEROS OF
A CLASS OF RANDOM HYPERBOLIC POLYNOMIAL

Mina Ketan Mahanti$^1$, Lokanath Sahoo$^2$
$^1$Department of Mathematics
College of Basic Science and Humanities
Orissa University of Agriculture and Technology
Bhubaneswar, Odisha, 751003, INDIA
$^2$Gopabandu Science College
Atagarh, Odisha,


Abstract. Let $y_1(\omega),y_2(\omega),\dots,y_n(\omega)$ be independent and normally distributed random variables with mean zero and variance one. For large values of n, it is proved that the the expected number of times the random hyperbolic polynomial $y_1(\omega)sinh t+ y_2(\omega)sinh 2t+\cdots+y_n(\omega)sinh nt$ crosses the line y=K is (1/$\pi$) log n +O(1) as long as $0\le K\le \sqrt{n}$.

Received: September 14, 2013

AMS Subject Classification: 60H99, 26C99

Key Words and Phrases: random polynomial, expected number of zeros, Kac-Rice formula

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DOI: 10.12732/ijpam.v97i1.2 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 97
Issue: 1
Pages: 13 - 19


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