Variance of real zeros of random orthogonal polynomials for varying and exponential weights
Electronic Journal of Probability(2022)
摘要
We determine the asymptotics for the variance of the number of zeros of random linear combinations of orthogonal polynomials of degree at most n associated with varying weights {e-2nQn}, with Gaussian coefficients. We deduce asymptotics of the variance for fixed exponential weights e(-2Q). In particular, we show that very generally, the variance is asymptotic to Cn, where the constant C involves a universal constant and an equilibrium density associated with the weight(s).
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关键词
Random orthogonal polynomials, exponential weights, variance of real zeros
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