Abstract. We address the important question of the extent to which random variables and vectors with truncated power tails retain the characteristic features of random variables and vectors with power tails. We define two truncation regimes, soft truncation regime and hard truncation regime, and show that, in the soft truncation regime, truncated power tails behave, in important respects, as if no truncation took place. On the other hand, in the had truncation regime much of "heavy tailedness" is lost. We show how to estimate consistently the tail exponent when the tails are truncated, and suggest statistical tests to decide on whether the truncation is soft or hard. Finally, we apply our methods to two recent data sets arising from computer networks.

Random matrices whose entries come from a stationary Gaussian process are studied. The limiting behavior of the eigenvalues as the size of the matrix goes to infinity is the main subject of interest in this work. It is shown that the limiting spectral distribution is determined by the absolutely continuous component of the spectral measure of the stationary process, a phenomenon resembling that in the situation where the entries of the matrix are i.i.d. On the other hand, the discrete component contributes to the limiting behavior of the eigenvalues in a completely different way. Therefore, this helps to define a boundary between short and long range dependence of a stationary Gaussian process in the context of random matrices.Comment: 50 pages. The current article generalises the results in http://arxiv.org/abs/1304.3394 and gives a new perspective and elegant proofs of some of the results there. It is to appear in Random Matrices: Theory and Application

Abstract. Stable laws can be tempered by modifying the Lévy measure to cool the probability of large jumps. Tempered stable laws retain their signature power law behavior at infinity, and infinite divisibility. This paper develops random walk models that converge to a tempered stable law under a triangular array scheme. Since tempered stable laws and processes are useful in statistical physics, these random walk models can provide a basic physical model for the underlying physical phenomena.

India is one of the first countries to introduce salt iodisation, but the national programme has experienced major setbacks. The purpose of this paper is to review the national efforts towards universal salt iodisation (USI) in India and highlight key challenges in programme implementation. A brief historical overview of the salt iodisation programme is provided and the current status of the household usage of iodised salt and population iodine status is described. The present status of the USI programme together with the challenges being faced towards achieving USI are classified in five categories, which represent the five guiding principles crucial to sustained USI programme success: ensuring political commitment, forming partnerships and coalition, ensuring availability of adequately iodised salt, strengthening the monitoring system and maintaining continuous advocacy, education and communication. A future agenda towards the achievement of USI is also proposed.

India is within striking reach of achieving universal salt iodisation. However, significant differentials by rural/urban, zonal and socio-economic indicators exist, warranting accelerated efforts and targeted interventions for high-risk groups.