Translator Disclaimer
2015 On expected number of level crossings of a random hyperbolic polynomial
Mina Ketan Mahanti, Loknath Sahoo
Rocky Mountain J. Math. 45(4): 1197-1208 (2015). DOI: 10.1216/RMJ-2015-45-4-1197

Abstract

Let $g_1(\omega),g_2(\omega),\ldots, g_n(\omega)$ be independent and normally distributed random variables with mean zero and variance one. We show that, for large values of $n$, the expected number of times the random hyperbolic polynomial $y=g_1(\omega)\cosh x+ g_2(\omega)\cosh 2x+\cdots +g_n(\omega)\cosh nx$ crosses the line $y=L$, where $L$ is a real number, is $\frac{1}{\pi}\log n +O(1)$ if $L=o(\sqrt{n})$ or ${L}/{\sqrt{n}} =O(1)$, but decreases steadily as $O(L)$ increases in magnitude and ultimately becomes negligible when $n^{-1}\log {L}/{\sqrt{n}}\to\infty$.

Citation

Download Citation

Mina Ketan Mahanti. Loknath Sahoo. "On expected number of level crossings of a random hyperbolic polynomial." Rocky Mountain J. Math. 45 (4) 1197 - 1208, 2015. https://doi.org/10.1216/RMJ-2015-45-4-1197

Information

Published: 2015
First available in Project Euclid: 2 November 2015

zbMATH: 1337.60044
MathSciNet: MR3418190
Digital Object Identifier: 10.1216/RMJ-2015-45-4-1197

Subjects:
Primary: 60H99
Secondary: 26C99

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
12 PAGES


SHARE
Vol.45 • No. 4 • 2015
Back to Top