Cycle length distributions in random permutations with diverging cycle weights
نویسندگان
چکیده
منابع مشابه
Cycle length distributions in random permutations with diverging cycle weights
We study the model of random permutations with diverging cycle weights, which was recently considered by Ercolani and Ueltschi, and others. Assuming only regular variation of the cycle weights we obtain a very precise local limit theorem for the size of a typical cycle, and use this to show that the empirical distribution of properly rescaled cycle lengths converges in probability to a gamma di...
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We consider the distribution of cycles in two models of random permutations, that are related to one another. In the first model, cycles receive a weight that depends on their length. The second model deals with permutations of points in the space and there is an additional weight that involves the length of permutation jumps. We prove the occurrence of infinite macroscopic cycles above a certa...
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We investigate the typical cycle lengths, the total number of cycles, and the number of finite cycles in random permutations whose probability involves cycle weights. Typical cycle lengths and total number of cycles depend strongly on the parameters, while the distributions of finite cycles are usually independent Poisson random variables. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 44,...
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where (θ1, θ2, . . .)≡ θ are real nonnegative numbers, rj (π) denotes the number of j -cycles in π [we always have ∑ j jrj (π) = n] and hn is the normalization. We are mainly interested in the distribution of cycle lengths in the limit n→∞ and in how these lengths depend on the set of parameters θ . The probability P is really a probability on sequences r = (r1, r2, . . .) that satisfy ∑ j jrj ...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2013
ISSN: 1042-9832
DOI: 10.1002/rsa.20520