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    Tests for covariance matrices, particularly for high dimensional data

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    Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can be larger than the sample size, n. The statistics, derived under very general conditions, follow an approximate normal distribution for large p, also when p >> n. Simulation results, particularly emphasizing the case when p can be much larger than n, show that the proposed statistics are accurate for both size control and power. A discussion of the commonly used assumptions for high dimensional set up is also given, with the conclusions applicable in general as well as in the special case of high dimensional covariance testing

    More on Five Dimensional EVH Black Rings

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    In this paper we continue our analysis of arXiv:1308.1478[hep-th] and study in detail the parameter space of three families of doubly spinning black ring solutions: balanced black ring, unbalanced ring and dipole-charged balanced black rings. In all these three families the Extremal Vanishing Horizon (EVH) ring appears in the vanishing limit of the dimensionful parameter of the solution which measures the ring size. We study the near horizon limit of the EVH black rings and for all three cases we find a (pinching orbifold) AdS3_3 throat with the AdS3_3 radius 2=8G5M/(3π)\ell^2=8 G_5 M/(3\pi) where MM is the ring mass and G5G_5 is the 5d Newton constant. We also discuss the near horizon limit of near-EVH black rings and show that the AdS3_3 factor is replaced with a generic BTZ black hole. We use these results to extend the EVH/CFT correspondence for black rings, a 2d CFT dual to near-EVH black rings.Comment: 30 page