Random polynomials of high degree and Levy concentration of measure

Random Polynomials of High Degree and Levy Concentration of Measure

We show that the Lp norms of random sequences of holomorphic sections sN ∈ H(M, L ) of powers of a positive line bundle L over a compact Kähler manifold M satisfy ‖sN‖p/‖sN‖2 = { O(1) for 2 ≤ p < ∞ O( √ logN) for p = ∞ } almost surely. This estimate also holds for almost-holomorphic sections of positive line bundles on symplectic manifolds (in the sense of our previous work) and we give almost ...

On Classifications of Random Polynomials

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

New Methods Providing High Degree Polynomials with Small Mahler Measure

the relationship between academic self-concept and academic achievement in english and general subjects of the students of high school

according to research, academic self-concept and academic achievement are mutually interdependent. in the present study, the aim was to determine the relationship between the academic self-concept and the academic achievement of students in english as a foreign language and general subjects. the participants were 320 students studying in 4th grade of high school in three cities of noor, nowshah...

Anti-concentration for random polynomials

We prove anti-concentration results for polynomials of independent Rademacher random variables, with arbitrary degree. Our results extend the classical Littlewood-Offord result for linear polynomials, and improve several earlier estimates. As an application, we address a challenge in complexity theory posed by Razborov and Viola.