Our interest in this paper is to explore limit theorems for various geometric functionals of excursion sets of isotropic Gaussian random fields. In the past, limit theorems have been proven for various geometric functionals of excursion sets/sojourn times ( see [4, 13, 14, 18, 22, 25] for a sample of works in such settings). The most recent addition being [6] where a central limit theorem (CLT)...

We show central limit theorems (CLT) for the linear statistics of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of α-stable laws and entries with moments exploding with the dimension, as in the adjacency matrices of Erdös-Rényi graphs. For the second model, we also prove a central limit theorem of the moments of its empirical eigenvalues...

We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This pro...

This paper introduces the theory of communicative competence by Hymes, the interpretation of communicative competence by Canale & Swain, the elements of efficient communication by Widdowson respectively, and the limitation of the previous application in China with the teaching environment of Classroom plus blackboard, analyzes the necessity and feasibility of creating authentic communicative en...

For Dynamical Systems, a strong bound on multiple correlations implies the Central Limit Theorem (CLT) [ChMa]. In Chernov’s paper [Ch2], such a bound is derived for dynamically Hölder continuous observables of dispersing Billiards. Here we weaken the regularity assumption and subsequently show that the bound on multiple correlations follows directly from the bound on pair correlations. Thus, a ...

We introduce a new version of Stein’s method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and concentration of measure. Unlike Skorokhod embeddings, the object whose variance has to be bounded has an explicit formula that makes it possible to carry out the program more easily. As an applicatio...

We give a closer look at the Central Limit Theorem (CLT) behavior in quasistationary states of the Hamiltonian Mean Field model, a paradigmatic one for long-range-interacting classical many-body systems. We present new calculations which show that, following their time evolution, we can observe and classify three kinds of long-standing quasi-stationary states (QSS) with different correlations. ...

A database search revealed extensive sequence similarity between Streptomyces lividans plasmid pIJ101 and Streptomyces plasmid pSB24. 2, which is a deletion derivative of Streptomyces cyanogenus plasmid pSB24.1. The high degree of relatedness between the two plasmids allowed the construction of a genetic map of pSB24.2, consisting of putative transfer and replication loci. Two pSB24.2 loci, nam...

Skin smear bacteriological examination results of 11,255 paucibacillary leprosy patients from 8 leprosy control units under the National Leprosy Eradication Programme (NLEP) in South India and the Outpatient Department (OPD) of the Central Leprosy Teaching & Research Institute (CLT&RI), Chengalpattu, between 1987 and 1989 were collected and analysed. Only 0.05% of the smears from leprosy contro...

We extend the sliding block code in symbolic dynamics to transform two sequences of Markov chains with time delay. Under the assumption that chains are irreducible and aperiodic, we prove the central limit theorem (CLT) for the normalized sums of extended sliding block codes from two sequences of Markov chains. We apply the theorem to evaluations of bit error probabilities in asynchronous sprea...