This paper studies a special type of binomial splitting process. Such a processcan be used to model a high dimensional corner parking problem as well asdetermining the depth of random PATRICIA (practical algorithm to retrieveinformation coded in alphanumeric) tries, which are a special class of digitaltree data structures. The latter also has natural interpretations in terms ofdistinct values in independent and identically distributed geometric randomvariables and the occupancy problem in urn models. The correspondingdistribution is marked by a logarithmic mean and a bounded variance, which isoscillating, if the binomial parameter p is not equal to ½, andasymptotic to one in the unbiased case. Also, the limiting distribution doesnot exist as a result of the periodic fluctuations.
"A binomial splitting process in connection with corner parking problems." J. Appl. Probab. 51 (4) 971 - 989, December 2014.