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We prove a Chevet type inequality which gives an upper bound for the norm of an isotropic log-concave unconditional random matrix in terms of expectation of the supremum of "symmetric exponential" processes compared to the Gaussian ones in the Chevet inequality.
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R. Adamczak, R. Latała, A.E. Litvak, A. Pajor and N. Tomczak-Jaegermann, Tail estimates for norms of sums of log-concave random vectors , preprint
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R. Adamczak, R. Latała, A.E. Litvak, A. Pajor and N. Tomczak-Jaegermann, Geometry of log-concave Ensembles of random matrices and approximate reconstruction , C.R. Math. Acad. Sci. Paris, to appear
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S. Mendelson and G. Paouris, Empirical Processes and isotropic, log-concave measures , preprint
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M. Talagrand, The generic chaining. Upper and lower bounds of stochastic processes , Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2005
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R. Latała, On weak tail domination of random vectors , Bull. Polish Acad. Sci. Math. 57
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R. Adamczak, A.E. Litvak, A. Pajor and N. Tomczak-Jaegermann, Quantitative estimates of the convergence of the empirical covariance matrix in log-concave Ensembles , Journal of AMS, 234
2010
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