41 citations · 98 across the 8 of their papers we have counts for
16 papers
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…
Singularity analysis, Hadamard products, and tree recurrences
James Allen Fill, Philippe Flajolet, Nevin Kapur
We present a toolbox for extracting asymptotic information on the coefficients of combinatorial generating functions. This toolbox notably includes a treatment of the effect of Had…
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…