Abstract
Letn distinguishable balls be placed randomly inton cells. IfM n denotes the maximal number of balls falling into the same cell, it is shown that asymptoticallyM n only attains two values: There is a sequencem n of integers such thatP(M n=mn orM n=mn+1) tends to 1, asn→∞.m n is determined explicitly and asymptotically.
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Stadje, W. A nearly degenerate random variable occurring in an occupancy problem. Monatshefte für Mathematik 108, 201–209 (1989). https://doi.org/10.1007/BF01308671
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DOI: https://doi.org/10.1007/BF01308671