On real zeros of random polynomials with hyperbolic elements (Q1384253)

Summary: This paper provides the asymptotic estimate for the expected number of real zeros of a random hyperbolic polynomial \(g_1 \text{cosh} x +2g_2 \text{cosh} 2x + \cdots +ng_n \text{cosh} nx\) where \(g_j\) \((j=1,2, \dots,n)\) are independent normally distributed random variables with mean zero and variance one. It is shown that for sufficiently large \(n\) this asymptotic value is \((1/ \pi)\log n\).