J. Kubilius, Probabilistic Methods in the Theory of Numbers, American Mathematical Society, Providence, Rhode Island, 1964. 21 Home/Search Document Not in Database Summary Related Articles Check |
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Large Deviations of Combinatorial Distributions I: Central Limit.. - Hwang (1995) (9 citations) (Correct)
....4. Set construction: A ( 1) In the last two cases, the radius of convergence of C is supposed to satisfy 1. A result parallel to Theorem 3 can be derived by replacing a log n with a log log n. This will have important applications to some additive arithmetical functions, cf. [26]. 4.2 Algebraico logarithmic scheme Next, let us consider generating functions of the form 1 (1 wG(z) 1 (G(0) 0) 13 where 2 N, 0, and 0. De ne a random variable n by its moment generating function n = mg e ms ]P (e ; z) P (1; z) 29) De nition. ....
....log n (e z=2 1) z=4 (2 e ) O uniformly for jzj small. Writing F n (x) Prf n log n x 4 log ng, Theorem 1 gives, for example, 1 F n (x) 1 (x) log n (y=2) for all x 0, x = o( 4 p log n) where is as in Theorem 2. For many other examples, cf. 18, Chs. 9,10 ] [8, 26]. Example 5. Meromorphic functions. The Eulerian numbers A(n; k) are de ned by the generating function n;k 0 A(n; k)w k z w(1 w) w 1)z ; and they enumerate the number of permutations of size n having k rises. Let n denote the number of rises in a random permutation of size n, where ....
J. Kubilius, Probabilistic Methods in the Theory of Numbers, American Mathematical Society, Providence, Rhode Island, 1964. 21
Large Deviations of Combinatorial Distributions I: Central Limit.. - Hwang (1995) (9 citations) (Correct)
....4. Set construction: # (# 1) In the last two cases, the radius of convergence # of C is supposed to satisfy # 1. A result parallel to Theorem 3 can be derived by replacing a log n with a log log n. This will have important applications to some additive arithmetical functions, cf. [26]. 4.2 Algebraico logarithmic scheme Next, let us consider generating functions of the form 1 wG(z) 1 (G(0) 0) 13 where # N, # 0, and # # 0. Define a random n by its moment generating function n = m e ms ]P (e , z) P (1, z) 29) Definition. 1 regular ....
....M n (z) E e #nz 2 # log n (e z 2 1) z 4 ) O small. Writing F n (x) Pr # n # log n x log n , Theorem 1 gives, for example, 2 log n #(y 2) for all x 0, x = o( # log n) where # is as in Theorem 2. For many other examples, cf. 18, Chs. 9,10 ] [8, 26]. Example 5. Meromorphic functions. The Eulerian numbers A(n, k) are defined by the generating function n,k#0 A(n, k)w k z w(1 w) w 1)z , and they enumerate the number of permutations of size n having k rises. Let# n denote the number of rises in a random permutation of size n, ....
J. Kubilius, Probabilistic Methods in the Theory of Numbers, American Mathematical Society, Providence, Rhode Island, 1964. 21
Distribution of Multiplicative Functions Defined on.. - Indlekofer, Manstavicius (Correct)
....for functions de ned on them. In his own words: It may be interesting to develop a more general theory of distribution functions of additive or multiplicative functions, on the basis of Axiom A , parallel to the theory for ordinary arithmetical function expounded in the book by Kubilius [13], and the papers of Billingsley [2] and Galambos [3] see Some of Open Questions of the book [12] Since its appearance a lot has been done in this direction. J.Knopfmacher was always in touch with the contributors. The rst of the authors of the present remark had a possibility to share ....
J.Kubilius, Probabilistic Methods in the Theory of Numbers, Amer. Math. Soc. Translations of Math. Monographs, 11, Providence, 1962.
Large deviations of combinatorial distributions II: Local limit.. - Hwang (1997) (11 citations) (Correct)
No context found.
J. Kubilius, Probabilistic methods in the theory of numbers, American Mathematical Society, Providence, Rhode Island, 1964. 19
Limit Theorems for Mergesort - Hwang (1996) (1 citation) (Correct)
No context found.
J. Kubilius, Probabilistic methods in the theory of numbers, Translations of Mathematical Monographs, Volume 11, AMS, Providence, Rhode Island, 1964.
Large deviations of combinatorial distributions II: Local limit.. - Hwang (1997) (11 citations) (Correct)
No context found.
J. Kubilius, Probabilistic methods in the theory of numbers, American Mathematical Society, Providence, Rhode Island, 1964. 19
Limit Theorems for Mergesort - Hwang (1996) (1 citation) (Correct)
No context found.
J. Kubilius, Probabilistic methods in the theory of numbers, Translations of Mathematical Monographs, Volume 11, AMS, Providence, Rhode Island, 1964.
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