منابع مشابه
Sum rules via large deviations
In the theory of orthogonal polynomials, sum rules are remarkable relationships between a functional defined on a subset of all probability measures involving the reverse KullbackLeibler divergence with respect to a particular distribution and recursion coefficients related to the orthogonal polynomial construction. Killip and Simon (Killip and Simon (2003)) have given a revival interest to thi...
متن کاملLarge Deviations for Random Spectral Measures and Sum Rules
We prove a Large Deviation Principle for the random spectral measure associated to the pair (HN , e) where HN is sampled in the GUE and e is a fixed unit vector (and more generally in the β extension of this model). The rate function consists of two parts. The contribution of the absolutely continuous part of the measure is the reversed Kullback information with respect to the semicircle distri...
متن کاملSum rules and large deviations for spectral matrix measures
A sum rule relative to a reference measure on R is a relationship between the reversed Kullback-Leibler divergence of a positive measure on R and some non-linear functional built on spectral elements related to this measure (see for example Killip and Simon 2003). In this paper, using only probabilistic tools of large deviations, we extend the sum rules obtained in Gamboa, Nagel and Rouault (20...
متن کاملSum rules and large deviations for spectral measures on the unit circle
This work is a companion paper of [26] and [25] (see also [11]). We continue to explore the connections between large deviations for random objects issued from random matrix theory and sum rules. Here, we are concerned essentially with measures on the unit circle whose support is an arc that is possibly proper. We particularly focus on two matrix models. The first one is the Gross-Witten ensemb...
متن کاملThe Probability of Large Deviations Forthe Sum Functions of Spacings
Let 0= U0,n ≤ U1,n ≤ ··· ≤ Un−1,n ≤ Un,n = 1 be an ordered sample from uniform [0,1] distribution, and Din = Ui,n −Ui−1,n, i = 1,2, . . . ,n; n = 1,2, . . . , be their spacings, and let f1n, . . . , fnn be a set of measurable functions. In this paper, the probabilities of the moderate and Cramer-type large deviation theorems for statistics Rn(D)= f1n(nD1n) + ···+ fnn(nDnn) are proved. Applicati...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2016
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2015.08.009