Maximum of the Characteristic Polynomial of Random Unitary Matrices
نویسندگان
چکیده
منابع مشابه
On the Characteristic Polynomial of a Random Unitary Matrix
We present a range of fluctuation and large deviations results for the logarithm of the characteristic polynomial Z of a random N ×N unitary matrix, as N → ∞. First we show that lnZ/ √ 1 2 lnN , evaluated at a finite set of distinct points, is asymptotically a collection of i.i.d. complex normal random variables. This leads to a refinement of a recent central limit theorem due to Keating and Sn...
متن کاملTruncations of random unitary matrices
We analyse properties of non-Hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N > M , distributed according to the Haar measure. In this way we define ensembles of random matrices and study the statistical properties of the spectrum located inside the unit circle. In the limit of large matrices, this ensemble is characterized by the ...
متن کاملextensions of some polynomial inequalities to the polar derivative
توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولThe characteristic polynomial of a random unitary matrix: a probabilistic approach
In this article, we propose a probabilistic approach to the study of the characteristic polynomial of a random unitary matrix. We recover the Mellin-Fourier transform of such a random polynomial, first obtained by Keating and Snaith in [8] using a simple recursion formula, and from there we are able to obtain the joint law of its radial and angular parts in the complex plane. In particular, we ...
متن کامل1 Moments of the characteristic polynomial in the three ensembles of random matrices Madan
Moments of the characteristic polynomial of a random matrix taken from any of the three ensembles, orthogonal, unitary or symplectic, are given either as a determinant or a pfaffian or as a sum of determinants. For gaussian ensembles comparing the two expressions of the same moment one gets two remarkable identities, one between an n × n determinant and an m × m determinant and another between ...
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: Communications in Mathematical Physics
سال: 2016
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-016-2740-6