Arratia, R., Stark, D., and Tavar e, S. (1995) Total variation asymptotics for Poisson process approximations of logarithmic combinatorial assemblies. Annals of Probability 23, 1347-- 1388.  Home/Search   Document Not in Database   Summary   Related Articles   Check

..... 26 Only the formul for d ##26216were previously obtained by Pfeifer [72] and Roos [76] All other results are new. For relevant materials on permutations, see Erdos and Turan [31] Wilf [92] Greene and Knuth [44] Arratia and Tavare [8] Knopfmacher and Warlimont [63] and Arratia et al. [7]; and on record values, Nevzorov [68] and Borovkov and Pfeifer [18] Random mappings. Structurally, random mappings are set of cycles of rooted labeled trees. In terms of the notation of 3.1, the generating function for the number of cycles (T structures) is given by (cf. 34, 65] 1 ....

....structure is very regular and partly because they exhibit many nice probabilistic properties which are analytically characterizable. Properties like invariant principle (cf. 5, 17, 26, 42, 47, 48, 49] order statistics (cf. 27, 50] Poisson approximation for component structures (cf. [5, 7, 8, 9]) etc, have been established for many special cases under stronger analytic settings. Our Poisson approximation for the class suggests the possibility of extending previous work under our general scheme. These and related problems will be investigated elsewhere. 40 ....

Arratia, R., Stark, D., and Tavar e, S. (1995) Total variation asymptotics for Poisson process approximations of logarithmic combinatorial assemblies. Annals of Probability 23, 1347-- 1388.

.... k (x) From the Poisson approximation formula (13) we can easily derive precise asymptotics for, say, the total variation distance n and a Poisson distribution with mean OE(n) Also our Theorem 1 is useful for further asymptotics of different probability metrics; cf. for example Arratia et al. [1] and the references cited there. 4 Combinatorial schemes of Flajolet and Soria In this section, we apply the theorems derived in previous sections to the combinatorial distributions studied by Flajolet and Soria [11, 12] These distributions are classified according to the type of singularity of ....

....or with some components appearing at most a specified number of times, etc. A detailed study in this direction can be found in [19] The uniformity afforded by the singularity analysis is also useful for other probabilistic properties of combinatorial parameters; see, for example, Arratia et al. [1] and Hansen [15] ....

R. Arratia, D. Stark and S. Tavar'e, Total variation asymptotics for Poisson process approximations of logarithmic combinatorial assemblies, Annals of Probability, 23, 1347--1388 (1995).

.... # k (x) From the Poisson approximation formula (13) we can easily derive precise asymptotics for, say, the total variation distance n and a Poisson distribution with mean #(n) Also our Theorem 1 is useful for further asymptotics of di#erent probability metrics; cf. for example Arratia et al. [1] and the references cited there. 4 Combinatorial schemes of Flajolet and Soria In this section, we apply the theorems derived in previous sections to the combinatorial distributions studied by Flajolet and Soria [11, 12] These distributions are classified according to the type of singularity of ....

....or with some components appearing at most a specified number of times, etc. A detailed study in this direction can be found in [19] The uniformity a#orded by the singularity analysis is also useful for other probabilistic properties of combinatorial parameters; see, for example, Arratia et al. [1] and Hansen [15] ....

R. Arratia, D. Stark and S. Tavare, Total variation asymptotics for Poisson process approximations of logarithmic combinatorial assemblies, Annals of Probability, 23, 1347--1388 (1995).

....d K and d L for Omega Gamma 26220 were previously obtained by Pfeifer [72] and Roos [76] All other results are new. For relevant materials on permutations, see Erdos and Tur an [31] Wilf [92] Greene and Knuth [44] Arratia and Tavar e [8] Knopfmacher and Warlimont [63] and Arratia et al. [7]; and on record values, Nevzorov [68] and Borovkov and Pfeifer [18] Random mappings. Structurally, random mappings are set of cycles of rooted labeled trees. In terms of the notation of x 3.1, the generating function for the number of cycles (T structures) is given by (cf. 34, 65] 1 1 ....

....structure is very regular and partly because they exhibit many nice probabilistic properties which are analytically characterizable. Properties like invariant principle (cf. 5, 17, 26, 42, 47, 48, 49] order statistics (cf. 27, 50] Poisson approximation for component structures (cf. [5, 7, 8, 9]) etc, have been established for many special cases under stronger analytic settings. Our Poisson approximation for the class CM suggests the possibility of extending previous work under our general scheme. These and related problems will be investigated elsewhere. 40 ....

Arratia, R., Stark, D., and Tavar' e, S. (1995) Total variation asymptotics for Poisson process approximations of logarithmic combinatorial assemblies. Annals of Probability 23, 1347-- 1388.

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