Random Matrix Ensembles Associated with Lax Matrices
نویسندگان
چکیده
منابع مشابه
q-RANDOM MATRIX ENSEMBLES
With a few notable exceptions, the interaction between the community of mathematicians who work in special functions, in particular, those that are in the area of q-series and basic Hypergeometric functions and the physics community has so far been minimal. In this review article, we will describe some developments in one area in physics, namely the Theory of Random Matrix Ensembles, where a q-...
متن کاملNew Multicritical Random Matrix Ensembles
In this paper we construct a class of random matrix ensembles labelled by a real parameter α ∈ (0, 1), whose eigenvalue density near zero behaves like |x|α. The eigenvalue spacing near zero scales like 1/N1/(1+α) and thus these ensembles are representatives of a continous series of new universality classes. We study these ensembles both in the bulk and on the scale of eigenvalue spacing. In the...
متن کاملRandom block matrices generalizing the classical ensembles
In this paper we consider random block matrices which generalize the classical Laguerre ensemble and the Jacobi ensemble. We show that the random eigenvalues of the matrices can be uniformly approximated by the roots of matrix orthogonal polynomials and obtain a rate for the maximum difference between the eigenvalues and the roots. This relation between the random block matrices and matrix orth...
متن کاملSpacing distributions in random matrix ensembles
The topic of spacing distributions in random matrix ensembles is almost as old as the introduction of random matrix theory into nuclear physics. Both events can be traced back to Wigner in the mid 1950’s [37, 38]. Thus Wigner introduced the model of a large real symmetric random matrix, in which the upper triangular elements are independently distributed with zero mean and constant variance, fo...
متن کاملFamily of generalized random matrix ensembles.
Using the generalized maximum entropy principle based on the nonextensive q entropy, a family of random matrix ensembles is generated. This family unifies previous extensions of random matrix theory (RMT) and gives rise to an orthogonal invariant stable Lévy ensemble with new statistical properties. Some of them are analytically derived.
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: Physical Review Letters
سال: 2009
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.103.054103