Random matrices, random polynomials and Coulomb systems
نویسندگان
چکیده
منابع مشابه
Random matrices, random polynomials and Coulomb systems
It is well known that the joint probability density of the eigenvalues of Gaussian ensembles of random matrices may be interpreted as a Coulomb gas. We review these classical results for hermitian and complex random matrices, with special attention devoted to electrostatic analogies. We also discuss the joint probability density of the zeros of polynomials whose coefficients are complex Gaussia...
متن کاملRandom Polynomials, Random Matrices and L-functions
We show that the Circular Orthogonal Ensemble of random matrices arises naturally from a family of random polynomials. This sheds light on the appearance of random matrix statistics in the zeros of the Riemann zeta-function.
متن کاملOn 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)+...
متن کاملRandom Polynomials, Random Matrices, and L-functions, Ii
We show that the Circular Orthogonal Ensemble of random matrices arises naturally from a family of random polynomials. This sheds light on the appearance of random matrix statistics in the zeros of the Riemann zeta-function.
متن کاملHyperelliptic curves, L-polynomials and random matrices
We analyze the distribution of unitarized L-polynomials L̄p(T ) (as p varies) obtained from a hyperelliptic curve of genus g ≤ 3 defined over Q. In the generic case, we find experimental agreement with a predicted correspondence (based on the Katz-Sarnak random matrix model) between the distributions of L̄p(T ) and of characteristic polynomials of random matrices in the compact Lie group USp(2g)....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Le Journal de Physique IV
سال: 2000
ISSN: 1155-4339
DOI: 10.1051/jp4:2000506