Geodesic
Two-stage allocations and the double \(Q\)-function
The electronic journal of combinatorics, Tome 10 (2003)
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Let $m+n$ particles be thrown randomly, independently of each other into $N$ cells, using the following two-stage procedure.1. The first $m$ particles are allocated equiprobably, that is, the probability of a particle falling into any particular cell is $1/N$. Let the $i$th cell contain $m_i$ particles on completion. Then associate with this cell the probability $a_i=m_i/m$ and withdraw the particles.2. The other $n$ particles are then allocated polynomially, that is, the probability of a particle falling into the $i$th cell is $a_i$.Let $\nu=\nu(m,N)$ be the number of the first particle that falls into a non-empty cell during the second stage. We give exact and asymptotic expressions for the expectation ${\bf E}\nu$.
DOI : 10.37236/1714
Classification : 05A16, 60C05, 05A15
Mots-clés : particles, probability, asymptotic expressions 
@article{10_37236_1714,
     author = {Sergey Agievich},
     title = {Two-stage allocations and the double {\(Q\)-function}},
     journal = {The electronic journal of combinatorics},
     year = {2003},
     volume = {10},
     doi = {10.37236/1714},
     zbl = {1023.05011},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1714/}
}
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%J The electronic journal of combinatorics
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Sergey Agievich. Two-stage allocations and the double \(Q\)-function. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1714

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