If G is a finite, directed, simple and irreducible graph, deletion of an edge makes the entropy decrease. We give a proof of this fact that avoids the Perron-Frobenius theorem and makes use of a technique developed by Gromov.
On a lemma of Littlewood and Offord on the distributions of linear combinations of vectors
β Scribed by Daniel J Kleitman
- Publisher
- Elsevier Science
- Year
- 1970
- Tongue
- English
- Weight
- 144 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0001-8708
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## Abstract Let __S__ denote the set of normalized univalent functions in the unit disk. We consider the problem of finding the radius of convexity __r~Ξ±~__ of the set {(1 β __Ξ±__)__f__(__z__) + __Ξ±zf__β²(__z__) : __f__ β __S__} for fixed __Ξ±__ β β. Using a linearization method we find the exact
In this paper a series representation of the joint density and the joint distribution of a quadratic form and a linear form in normal variables is developed. The expansion makes use of Laguerre polynomials. As an example the calculation of the joint distribution of the mean and the sample variance i