m-ary search trees when m ≥ 27 : a strong asymptotics for the space requirements ( updated version , september 03 )

@inproceedings{ChauvinmaryST,
  title={m-ary search trees when m ≥ 27 : a strong asymptotics for the space requirements ( updated version , september 03 )},
  author={Brigitte Chauvin and Nicolas Pouyanne}
}
It is known that the joint distribution of the number of nodes of each type of an m-ary search tree is asymptotically multivariate normal when m ≤ 26. When m ≥ 27, we show the following strong asymptotics of the random vector Xn = (X (1) n , . . . , X (m−1) n ), where X (i) n denotes the number of nodes containing i− 1 keys after having introduced n− 1 keys in the tree: there exist (nonrandom) vectors X, C and S and random variables ρ and φ such that 
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