Nonuniversality of compact support probability distributions in random matrix theory.
نویسندگان
چکیده
The two-point resolvent is calculated in the large-n limit for the generalized fixed and bounded trace ensembles. It is shown to disagree with that of the canonical Gaussian ensemble by a nonuniversal part that is given explicitly for all monomial potentials V(M)=M(2p). Moreover, we prove that for the generalized fixed and bounded trace ensemble all k-point resolvents agree in the large-n limit, despite their nonuniversality.
منابع مشابه
Compact support probability distributions in random matrix theory
We consider a generalization of the fixed and bounded trace ensembles introduced by Bronk and Rosenzweig up to an arbitrary polynomial potential. In the large-n limit we prove that the two are equivalent and that their eigenvalue distribution coincides with that of the ”canonical” ensemble with measure exp[-nTr V(M)]. The mapping of the corresponding phase boundaries is illuminated in an explic...
متن کاملHow to generate random matrices from the classical compact groups
We discuss how to generate random unitary matrices from the classical compact groups U(N), O(N) and USp(2N) with probability distributions given by the respective invariant measures. The algorithm is straightforward to implement using standard linear algebra packages. This approach extends to the Dyson circular ensembles too. This article is based on a lecture given by the author at the summer ...
متن کاملFUZZY INFORMATION AND STOCHASTICS
In applications there occur different forms of uncertainty. The twomost important types are randomness (stochastic variability) and imprecision(fuzziness). In modelling, the dominating concept to describe uncertainty isusing stochastic models which are based on probability. However, fuzzinessis not stochastic in nature and therefore it is not considered in probabilisticmodels.Since many years t...
متن کاملCommutative Monads as a Theory of Distributions
It is shown how the theory of commutative monads provides an axiomatic framework for several aspects of distribution theory in a broad sense, including probability distributions, physical extensive quantities, and Schwartz distributions of compact support. Among the particular aspects considered here are the notions of convolution, density, expectation, and conditional probability.
متن کاملDetermination of Maximum Bayesian Entropy Probability Distribution
In this paper, we consider the determination methods of maximum entropy multivariate distributions with given prior under the constraints, that the marginal distributions or the marginals and covariance matrix are prescribed. Next, some numerical solutions are considered for the cases of unavailable closed form of solutions. Finally, these methods are illustrated via some numerical examples.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
دوره 60 5 Pt A شماره
صفحات -
تاریخ انتشار 1999