A Probabilistic Version of Eneström–Kakeya Theorem for Certain Random Polynomials

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

A random version of Sperner's theorem

Let P(n) denote the power set of [n], ordered by inclusion, and let P(n, p) be obtained from P(n) by selecting elements from P(n) independently at random with probability p. A classical result of Sperner [12] asserts that every antichain in P(n) has size at most that of the middle layer, ( n ⌊n/2⌋ ) . In this note we prove an analogous result for P(n, p): If pn → ∞ then, with high probability, ...

On Permanental Polynomials of Certain Random Matrices

The paper addresses the calculation of correlation functions of permanental polynomials of matrices with random entries. By exploiting a convenient contour integral representation of the matrix permanent some explicit results are provided for several random matrix ensembles. When compared with the corresponding formulae for characteristic polynomials, our results show both striking similarities...

A universality theorem for ratios of random characteristic polynomials

We consider asymptotics of ratios of random characteristic polynomials associated with orthogonal polynomial ensembles. Under some natural conditions on the measure in the definition of the orthogonal polynomial ensemble we establish a universality limit for these ratios. c ⃝ 2012 Elsevier Inc. All rights reserved.

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)+...