On the Expected Number of Zeros of a Random Harmonic Polynomial

Expected Number of Local Maxima of Some Gaussian Random Polnomials

On the average number of sharp crossings of certain Gaussian random polynomials

On Classifications of Random Polynomials

 Let $ a_0 (omega), a_1 (omega), a_2 (omega), dots, a_n (omega)$ be a sequence of independent random variables defined on a fixed probability space $(Omega, Pr, A)$. There are many known results for the expected number of real zeros of a polynomial $ a_0 (omega) psi_0(x)+ a_1 (omega)psi_1 (x)+, a_2 (omega)psi_2 (x)+...

Domain of attraction of normal law and zeros of random polynomials

Let$ P_{n}(x)= sum_{i=0}^{n} A_{i}x^{i}$ be a random algebraicpolynomial, where $A_{0},A_{1}, cdots $ is a sequence of independent random variables belong to the domain of attraction of the normal law. Thus $A_j$'s for $j=0,1cdots $ possesses the characteristic functions $exp {-frac{1}{2}t^{2}H_{j}(t)}$, where $H_j(t)$'s are complex slowlyvarying functions.Under the assumption that there exist ...

On the Zeros of Random Harmonic Polynomials: the Truncated Model

Inspired by Wilmshurst’s conjecture, W. Li and A. Wei (2009) initiated a probabilistic study concerning the zeros of harmonic polynomials. They derived a Kac-Rice type formula for the expected number of zeros of random harmonic polynomials p(z) + q(z) with independent Gaussian coefficients. They also provided asymptotics in the case when p and q are sampled independently from the the (complex) ...