41 citations · 98 across the 8 of their papers we have counts for
15 papers · 1 filter
A repertoire for additive functionals of uniformly distributed m-ary search trees
James Allen Fill, Nevin Kapur
Using recent results on singularity analysis for Hadamard products of generating functions, we obtain the limiting distributions for additive functionals on -ary search trees on…
The space requirement of m-ary search trees: distributional asymptotics for m >= 27
James Allen Fill, Nevin Kapur
We study the space requirement of -ary search trees under the random permutation model when is fixed. Chauvin and Pouyanne have shown recently that , the space…
Percolation, first-passage percolation, and covering times for Richardson's model on the n-cube
James Allen Fill, Robin Pemantle
Percolation with edge-passage probability p and first-passage percolation are studied for the n-cube B_n ={0,1}^n with nearest neighbor edges. For oriented and unoriented percolati…
Asymptotic analysis via Mellin transforms for small deviations in -norm of integrated Brownian sheets
James Allen Fill, Fred Torcaso
We use Mellin transforms to compute a full asymptotic expansion for the tail of the Laplace transform of the squared -norm of any multiply-integrated Brownian sheet. Through r…
Limiting distributions for additive functionals on Catalan trees
James Allen Fill, Nevin Kapur
Additive tree functionals represent the cost of many divide-and-conquer algorithms. We derive the limiting distribution of the additive functionals induced by toll functions of the…
Transfer Theorems and Asymptotic Distributional Results for m-ary Search Trees
James Allen Fill, Nevin Kapur
We derive asymptotics of moments and identify limiting distributions, under the random permutation model on m-ary search trees, for functionals that satisfy recurrence relations of…