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seba
seba
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Let us fix a number of urns $n$ and a fixed capacity $c$. I would like to know which is the probability that $m$ balls, thrown at random in $n$ urns, "overflow", in the sense that at least one urn has assigned $\geq c$ balls.

There are several results in the literature about the maximum number of balls in an urn (in particular, Raab and Steeger's 1999) paper), but the results are all asymptotic with high probability. I need a precise analytical result.

Let us fix a number of urns $n$ and a fixed capacity $c$. I would like to know which is the probability that $m$ balls, thrown at random in $n$ urns, "overflow", in the sense that at least one urn has assigned $\geq c$ balls.

There are several results in the literature about the maximum number of balls in an urn (in particular, Raab and Steeger's 1999) paper, but the results are all asymptotic with high probability. I need a precise analytical result.

Let us fix a number of urns $n$ and a fixed capacity $c$. I would like to know which is the probability that $m$ balls, thrown at random in $n$ urns, "overflow", in the sense that at least one urn has assigned $\geq c$ balls.

There are several results in the literature about the maximum number of balls in an urn (in particular, Raab and Steeger's 1999 paper), but the results are all asymptotic with high probability. I need a precise analytical result.

Source Link
seba
seba
  • 173
  • 6

What is the probability that throwing $m$ balls at random in $n$ urns at least one urn contains $c$ elements?

Let us fix a number of urns $n$ and a fixed capacity $c$. I would like to know which is the probability that $m$ balls, thrown at random in $n$ urns, "overflow", in the sense that at least one urn has assigned $\geq c$ balls.

There are several results in the literature about the maximum number of balls in an urn (in particular, Raab and Steeger's 1999) paper, but the results are all asymptotic with high probability. I need a precise analytical result.