On the Number of Real Zeros of a Random Trigonometric Polynomial
On the Number of Real Zeros of a Random Trigonometric Polynomial
For the random trigonometric polynomial \[ \sum \limits _{n = 1}^N {{g_n}(t)\cos n\theta ,} \] where ${g_n}(t),0 \leqslant t \leqslant 1$, are dependent normal random variables with mean zero, variance one and joint density function \[ |M{|^{1/2}}{(2\pi )^{ - N/2}}\exp [ - (1/2)\bar aâM\bar a]\] where ${M^{ - 1}}$ is …