A new proof of generalized theorem of Irving Weiss (Q1203457)

The classical occupancy theorem of Irving Weiss states that the number of unoccupied cells, if the number of balls and the number of cells approach infinity, is normal. The main multivariate theorem of the theory has been shown by \textit{B. A. Sevast'yanov} and \textit{V. P. Chist'yakov} [Theory Probab. Appl. 9(1964), 198-211 (1965); translation from Teor. Veroyatn. Primen. 9(1964), 223-237 (1964; Zbl 0142.147)] on the basis of \textit{A. Rényi's} paper [Publ. Math. Inst. Hung. Acad. Sci., Ser. A 7, 203-214 (1962; Zbl 0113.127)]. Here we show that the result may be improved using the multivariate local limit theorem. The presented result has been obtained as a by-product of the estimation of the number of nuclear genes in a model of respiratory deficiency in yeast.