Consider the random intervals In（W） ：= （wn -en/2,Wn ＋en/2）（mod 1） with their centers wn being i.i.d, but not necessary uniformly distributed on the circle T = R/Z and with their lengths decreasing to zero. Using the dimension theory in dynamical systems, we give conditions on which the circle is finitely or infinitely often covered by intervals {In （ w ） } n≥ 1.
