Asymptotic Normality in a Discrete Analog of the Parking Problem

摘要

The behavior of higher-order central moments in the discrete version of the “parking problem” is studied. For these moments, the asymptotic behavior is obtained as the length of the filled segment increases without limit. This enables to prove the asymptotic normality of the total length of the nested intervals of length l on a segment of length n for any fixed l > 2 with unlimited increase in n.