Spatial random permutations with small cycle weights
نویسندگان
چکیده
منابع مشابه
Spatial Random Permutations with Small Cycle Weights
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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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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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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We give an algorithm for learning a permutation on-line. The algorithm maintains its uncertainty about the target permutation as a doubly stochastic matrix. This matrix is updated by multiplying the current matrix entries by exponential factors. These factors destroy the doubly stochastic property of the matrix and an iterative procedure is needed to re-normalize the rows and columns. Even thou...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2009
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-009-0248-0