On the average number of real zeros of a class of random algebraic curves

Masilamani Sambandham

Vol. 81 (1979), No. 1, 207–215

DOI: 10.2140/pjm.1979.81.207

Abstract

Let a₁,a₂,⋯ , be a sequence of dependent normal random variables with mean zero, variance one and the correlation between any two random variables is ρ, 0 < ρ < 1. In this paper the average number of real zeros of ∑ _k=1ⁿa_kk^px^k, 0 ≦ p < ∞ is estimated for large n and this average is asymptotic to (2π)⁻¹[1 + (2p + 1)^1∕2]log n.

Mathematical Subject Classification 2000

Primary: 60G17

Milestones

Received: 20 April 1977

Published: 1 March 1979