We report on recent results on the spectral statistics of the discrete Anderson model in the localized phase obtained in [6]. In particular, we describe the • locally uniform Poisson behavior of the rescaled eigenvalues, • independence of the Poisson processes obtained as such limits at distinct energies, • locally uniform Poisson behavior of the joint distributions of the rescaled energies and...

This study investigated the distribution and randomness of numbers in square root 2. Rstudio was used extracting 2 up to 1,000 digits. The Chi-square test is for testing uniformity numbers, runs numbers. Results show that distributions generated n = 100 are uniform. sequence appears be random.

1. BASIC PROBABILITY THEORY 1.1 Measure-theoretical foundation of probability theory 1.2 Independence 1.3 Borel measurable functions 1.4 Mathematical expectatlon 1.5 Characteristic functions 1.6 Random functions 2. CONVERGENCE 2.1 Heak and strong convergence of random variables 2.2 Convergence of mathematical expectations 2.3 Convergence of distributions 2.4 Central limit theoreras 2.5 Further ...

objective: the aim of this study was to evaluate the influences of reconstruction and attenuation correction on the differences in the radioactivity distributions in 123i brain spect obtained by the hybrid spect/ct device. methods: we used the 3-dimensional (3d) brain phantom, which imitates the precise structure of gray mater, white matter and bone regions. it was filled with 123i solution (20...

We consider a family of random trees satisfying a Markov branching property. Roughly, this property says that the subtrees above some given height are independent with a law that depends only on their total size, the latter being either the number of leaves or vertices. Such families are parameterized by sequences of distributions on partitions of the integers, that determine how the size of a ...

Extended Abstract. The simplest and the most common way of comparing two random variables is through their means and variances. It may happen that in some cases the median of X is larger than that of Y, while the mean of X is smaller than the mean of Y. However, this confusion will not arise if the random variables are stochastically ordered. Similarly, the same may happen if one would like to ...

Let X1 X2 be a sequence of pairwise negatively dependent random variables with distributions F1 F2 on − , and let S n be the maximum of its first n partial sums S1 Sn. This article studies the asymptotic tail probabilities of Sn and S n . Under suitable regularity conditions on the distributions F1 Fn, we prove that both P Sn > x and P S n > x are asymptotic to ∑n i=1 1− Fi x as x → , indicatin...

We consider a family of random trees satisfying a Markov branching property. Roughly, this property says that the subtrees above some given height are independent with a law that depends only on their total size, the latter being either the number of leaves or vertices. Such families are parameterized by sequences of distributions on partitions of the integers, that determine how the size of a ...