On the covering by small random intervals
On the covering by small random intervals
Consider the random intervals In=ωn+(0,ℓn) (modulo 1) with their left points ωn independently and uniformly distributed over the interval [0,1)=R/Z and with their lengths decreasing to zero. We prove that the Hausdorff dimension of the set limnIn of points covered infinitely often is almost surely equal to 1/α when ℓn=a/nα …