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].