Real almost zeros of random polynomials with complex coefficients

[摘要] We present a simple formula for the expected numberof times that a complex-valued Gaussian stochastic process has azero imaginary part and the absolute value of its real part isbounded by a constant valueM. We show that only some mildconditions on the stochastic process are needed for our formula toremain valid. We further apply this formula to a random algebraicpolynomial with complex coefficients. We show how the aboveexpected value in the case of random algebraic polynomials variesfor different behaviour ofM.

[学科分类] 应用数学