An estimate of the second moment of a sampling of the Riemann zeta function on the critical line

We investigate the second moment of a random sampling ζ(1/2+iXt)ζ(1/2+iXt) of the Riemann zeta function on the critical line. Our main result states that if XtXt is an increasing random sampling with gamma distribution, then for all sufficiently large t,E|ζ(1/2+iXt)|2=logt+O(logtloglogt).