L. Takacs, The asymptotic distribution of the total heights of random rooted trees, Acta Sci. Math. 57 (1993), 613-625. Home/Search Document Not in Database Summary Related Articles Check |
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On the Analysis of Linear Probing Hashing - Flajolet, Poblete, Viola (1998) (29 citations) (Correct)
....also related to other contemporary works from the early 1980 s dealing with Brownian motion [34, 37] where Airy functions also crop up explicitly. R 2 ) Path length in trees. The path length of a tree is the sum of the distances of all nodes to the root of the tree. In a series of papers, Tak acs [41, 43] has established limit Airy distribution results for various families of trees including Cayley trees and Catalan trees as special cases, while rederiving independently in [40, 42] some of the results of Louchard. Regarding methods, our Theorem 3 establishes directly the Airy law for (P 1 ) by a ....
Tak' acs, L. The asymptotic distribution of the total heights of random rooted trees. Acta Scientifica Mathematica (Szeged) 57 (1993), 613--625.
The Average Case Analysis of Algorithms: Multivariate.. - Flajolet, SEDGEWICK (1997) (6 citations) (Correct)
....techniques yield a local limit law. The limit law of Xn = p n is of the Rayleigh type R( with density function, g(x) xe Gammax 2 =2 : 2 Example 37. Path length in trees. A final example is the distribution of path length in trees, that has been studied by Louchard, Takacs and others [44, 45, 58, 59]. The distribution is known not to be Gaussian as 9.9. EXTENSIONS 115 results from computation of the first few moments. In the case of general Catalan trees, the analysis reduces (cf Chapter 3) to that of the functional equation F (z; u) 1 1 Gamma zF (zu; u) This defines F (z; u) as a ....
....when u 1, then B(z; u) is an entire function of z, so that F (z; u) is meromorphic in z. Hence the singularity diagram: u = 1 Gamma ffl u = 1 u = 1 ffl ae(u) 1 4 ae(1) 1 4 ae(u) 0 Z Gamma1 Z 1=2 The limit law is an Airy distribution, that is related to Airy functions [44, 45, 58, 59]. By an analytical tour de force, Prellberg [51] has developed a method based on coalescing saddle points that permits us to extract such limits. As similar problems occur in relation to connectivity of random graphs, future years should see more applications of Prellberg s method. 2 Extremal ....
Tak' acs, L. The asymptotic distribution of the total heights of random rooted trees. Acta Scientifica Mathematica (Szeged) 57 (1993), 613--625.
Stochastic Analysis Of Tree-Like Data Structures - Drmota (2002) (Correct)
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L. Takacs, The asymptotic distribution of the total heights of random rooted trees, Acta Sci. Math. 57 (1993), 613-625.
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