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Random matrices and information theory

Случайные матрицы и теория информации

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Il Nuovo Cimento B (1965-1970)

Summary

A general method is proposed for assigning a probability distribution to a random matrix. Its principle is that the amount of information contained in the probability distribution should not exceed the minimum amount needed to satisfy relevant properties of the matrix. As examples, classical random matrices are recovered, and the case of a given density of eigenvalues is treated.

Riassunto

Si propone un metodo generale per attribuire una distribuzione di probabilità ad una matrice aleatoria. Il metodo si basa sul principio che la distribuzione di probabilità non debba contenere informazioni maggiori del minimo necessario per soddisfare le proprietà importanti della matrice. Come esempio, si ritrovano le matrici aleatorie classiche e si tratta il caso di una densità data di autovalori.

Реэюме

Предлагается обший метод для приписывания распределения вероятности для случайной матрицы. Суть метода состоит в том, что количество информации, содержашейся в распределении вероятности, не должно превыщать минимального количества, необходимого для удовлетворения соответствуюших свойств матрицы. Как пример, эаново выводятся классические случайные матрицы, и рассматривается случай для эаданной плотности собственных эначений.

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  1. Service de Physique Théorique, Centre d’Études Nucléaires de Saclay, Saclay

    R. Balian

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  1. R. Balian
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Balian, R. Random matrices and information theory. Nuovo Cimento B (1965-1970) 57, 183–193 (1968). https://doi.org/10.1007/BF02710326

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