This paper presents a statistical explanation of filament formation in
the Galactic atomic hydrogen. We claim that even in the absence of dy
namical factors, the Gaussian field corresponding to the measured valu
es of the spectrum of random density should develop filamentary struct
ure, the existence of which has long been claimed. Therefore, this pap
er shows that the filamentary structure of H I is consistent with the
shallow three-dimensional spectrum of random density obtained by Lazar
ian.