# Random permutations with logarithmic cycle weights

@article{Robles2018RandomPW, title={Random permutations with logarithmic cycle weights}, author={Nicolas Robles and Dirk Zeindler}, journal={arXiv: Probability}, year={2018} }

We consider random permutations on $\Sn$ with logarithmic growing cycles weights and study the asymptotic behavior as the length $n$ tends to infinity. We show that the cycle count process converges to a vector of independent Poisson variables and also compute the total variation distance between both processes. Next, we prove a central limit theorem for the total number of cycles. Furthermore we establish a shape theorem and a functional central limit theorem for the Young diagrams associated…

## 6 Citations

Multiplicative arithmetic functions and the generalized Ewens measure

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- 2019

Random integers, sampled uniformly from [1 , x ], share similarities with random permutations, sampled uniformly from S n . These similarities include the Erd˝os-Kac theorem on the distribution of…

Long cycle of random permutations with polynomially growing cycle weights

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The asymptotic behaviour of the long cycles under a multiplicative measure with polynomial growing cycle weights is determined and it is proved that the cumulative cycle numbers converge in the region of theLong cycles to a Poisson process.

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Since the seminal work of Keating and Snaith, the characteristic polynomial of a random Haar-distributed unitary matrix has seen several of its functional studied or turned into a conjecture; for…

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This study extends a prior investigation of limit shapes for partitions of integers, which was based on analysis of sums of geometric random variables. Here we compute limit shapes for grand…

Multiplicative arithmetic functions and the Ewens measure

- Mathematics
- 2019

Random integers, sampled uniformly from $[1,x]$, share similarities with random permutations, sampled uniformly from $S_n$. These similarities include the Erd\H{o}s-Kac theorem on the distribution of…

N T ] 2 S ep 2 01 9 Multiplicative arithmetic functions and the Ewens measure

- Mathematics
- 2019

Random integers, sampled uniformly from [1, x], share similarities with random permutations, sampled uniformly from Sn. These similarities include the Erdős-Kac theorem on the distribution of the…

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