by
Svante Janson

Citations: | 5 - 4 self |

@MISC{Janson00momentconvergence,

author = {Svante Janson},

title = {Moment Convergence In Conditional Limit Theorems},

year = {2000}

}

. Consider a sum P N 1 Y i of random variables conditioned on a given value of the sum P N 1 X i of some other variables, where X i and Y i are dependent but the pairs (X i ; Y i ) form an i.i.d. sequence. We prove, for a triangular array (X ni ; Y ni ) of such pairs satisfying certain conditions, both convergence of the distribution of the conditioned sum (after suitable normalization) to a normal distribution, and convergence of its moments. The results are motivated by an application to hashing with linear probing; we give also some other applications to occupancy problems, random forests, and branching processes. 1. Introduction Many random variables arising in different areas of probability theory, combinatorics and statistics turn out to have the same distribution as a sum of independent random variables conditioned on a specific value of another such sum. More precisely, we are concerned with variables with the distribution of P N 1 Y i conditioned on P N 1 X...

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