SUDAKOV MINORATION PRINCIPLE AND SUPREMUM OF SOME PROCESSES

Let X-i be a sequence of independent symmetric real random variables w ith logarithmically concave tails. We find a new version of Sudakov mi noration principle for estimating from below Esup(t is an element of T ) Sigma t(i)X(i). If we moreover assume that tails of X-i are of moder ate growth this enables us to give geometric conditions on set T equiv alent to boundedness of the process (Sigma t(i)X(i))(t is an element o f T) This generalize previous results of Talagrand [T4].