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We derive simple concentration inequalities for bounded random vectors, which generalize Hoeffdings inequalities for bounded scalar random variables. As applications, we apply the general results to multinomial and Dirichlet distributions to obtain multivariate concentration inequalities.
Consider $n$ complex random matrices $X_1,ldots,X_n$ of size $dtimes d$ sampled i.i.d. from a distribution with mean $E[X]=mu$. While the concentration of averages of these matrices is well-studied, the concentration of other functions of such matric
We prove a non-asymptotic concentration inequality for the spectral norm of sparse inhomogeneous random tensors with Bernoulli entries. For an order-$k$ inhomogeneous random tensor $T$ with sparsity $p_{max}geq frac{clog n}{n }$, we show that $|T-mat
We propose a new approach for deriving probabilistic inequalities based on bounding likelihood ratios. We demonstrate that this approach is more general and powerful than the classical method frequently used for deriving concentration inequalities su
In this paper, we study the asymptotic thin-shell width concentration for random vectors uniformly distributed in Orlicz balls. We provide both asymptotic upper and lower bounds on the probability of such a random vector $X_n$ being in a thin shell o
We obtain moment and Gaussian bounds for general Lipschitz functions evaluated along the sample path of a Markov chain. We treat Markov chains on general (possibly unbounded) state spaces via a coupling method. If the first moment of the coupling tim