Large Deviations of Empirical Measures of Zeros of Random Polynomials

Large deviations for zeros of random polynomials with i.i.d. exponential coefficients

We derive a large deviation principle for the empirical measure of zeros of the random polynomial Pn(z) = ∑n j=0 ξjz j , where the coefficients {ξj}j≥0 form an i.i.d. sequence of exponential random variables.

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 average number of sharp crossings of certain Gaussian random polynomials

Geometry and large deviations for zeros of Gaussian random holomor- phic polynomials on Riemann sur- faces

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)+...