# Random derangements and the Ewens Sampling Formula

arXiv: https://arxiv.org/abs/2006.04840 · HTML: https://mlsanity.com/paper/2006.04840/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2020.

## Built on by (most cited first, 1 of 1)

- [Temporal distribution of clusters of investors and their application in prediction with expert advice](https://mlsanity.com/paper/2406.19403/) (2024)

## Abstract (arXiv)

We study derangements of 1,2,ldots,n under the Ewens distribution with parameter θ. We give the moments and marginal distributions of the cycle counts, the number of cycles, and asymptotic distributions for large n. We develop a 0,1-valued non-homogeneous Markov chain with the property that the counts of lengths of spacings between the 1s have the derangement distribution. This chain, an analog of the so-called Feller Coupling, provides a simple way to simulate derangements in time independent of θ for a given n and linear in the size of the derangement.