Abstract: Let Mn be the maximum of n zero-mean gaussian variables X1, .., Xn with covariance matrix of minimum eigenvalue λ and maximum eigenvalue Λ. Then, for n ≥ 70, Pr{Mn ≥ λ (2 logn− 2.5− log(2 logn− 2.5)) 1 2 − .68Λ} ≥ 1 2 . Bounds are also given for tail probabilities other than 1 2 . Upper bounds are given for tail probabilities of the maximum of dependent identically distributed variabl...

in this paper we study the almost universal convergence of weighted sums for sequence {x ,n } of negatively dependent (nd) uniformly bounded random variables, where a, k21 is an may of nonnegative real numbers such that 0(k ) for every ?> 0 and e|x | f | =0 , f = ?(x ,…, x ) for every n>l.