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Approximation with a Poisson distribution

It is clear that a direct numerical evaluation of $ p_{0}$ is limited to the case of relatively small M and N. According to [28], it is possible to estimate $ p_{m}$, the probability to have exactly m cells empty, with a Poisson distribution.

$\displaystyle \lambda=M e^{-\frac{N}{M}}$

$\displaystyle p_{m}(N,M)= e^{-\lambda} \frac{\lambda^m}{m!}$

In our case, we use $ m=0$ to get all cells occupied:

$\displaystyle p_{0}(N,M) = e^{-\lambda}$

Tiziano Mengotti 2004-03-27