---
OA_place: repository
OA_type: green
_id: '20572'
abstract:
- lang: eng
  text: "We present an elementary non-recursive formula for the multivariate moments\r\nof
    the Dirichlet distribution on the standard simplex, in terms of the pattern\r\ninventory
    of the moments' exponents. We obtain analog formulas for the\r\nmultivariate moments
    of the Dirichlet-Ferguson and Gamma measures. We further\r\nintroduce a polychromatic
    analogue of Ewens sampling formula on colored integer\r\npartitions, discuss its
    relation with suitable extensions of Hoppe's urn model\r\nand of the Chinese restaurant
    process, and prove that it satisfies an adapted\r\nnotion of consistency in the
    sense of Kingman."
acknowledgement: This research was funded by the Austrian Science Fund (FWF) ESPRIT
  208. For the purpose of open access, the authors have applied a CC BY public copyright
  licence to any Author Accepted Manuscript version arising from this submission.
  F.Q. gratefully acknowledges support by the Austrian Science Fund (FWF), Project
  SFB F65. The authors are grateful to Professor Nathanaël Berestycki for several
  helpful suggestions, and to Nicola Battisti and Dr. Elizabeth Hollwey for enlightening
  discussions on DNA-methylation.
article_number: '2309.11292'
article_processing_charge: No
arxiv: 1
author:
- first_name: Lorenzo
  full_name: Dello Schiavo, Lorenzo
  id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
  last_name: Dello Schiavo
  orcid: 0000-0002-9881-6870
- first_name: Filippo
  full_name: Quattrocchi, Filippo
  id: 3ebd6ba8-edfb-11eb-afb5-91a9745ba308
  last_name: Quattrocchi
  orcid: 0009-0000-9773-1931
citation:
  ama: Dello Schiavo L, Quattrocchi F. Multivariate Dirichlet moments and a polychromatic
    Ewens sampling formula. <i>arXiv</i>. doi:<a href="https://doi.org/10.48550/arXiv.2309.11292">10.48550/arXiv.2309.11292</a>
  apa: Dello Schiavo, L., &#38; Quattrocchi, F. (n.d.). Multivariate Dirichlet moments
    and a polychromatic Ewens sampling formula. <i>arXiv</i>. <a href="https://doi.org/10.48550/arXiv.2309.11292">https://doi.org/10.48550/arXiv.2309.11292</a>
  chicago: Dello Schiavo, Lorenzo, and Filippo Quattrocchi. “Multivariate Dirichlet
    Moments and a Polychromatic Ewens Sampling Formula.” <i>ArXiv</i>, n.d. <a href="https://doi.org/10.48550/arXiv.2309.11292">https://doi.org/10.48550/arXiv.2309.11292</a>.
  ieee: L. Dello Schiavo and F. Quattrocchi, “Multivariate Dirichlet moments and a
    polychromatic Ewens sampling formula,” <i>arXiv</i>. .
  ista: Dello Schiavo L, Quattrocchi F. Multivariate Dirichlet moments and a polychromatic
    Ewens sampling formula. arXiv, 2309.11292.
  mla: Dello Schiavo, Lorenzo, and Filippo Quattrocchi. “Multivariate Dirichlet Moments
    and a Polychromatic Ewens Sampling Formula.” <i>ArXiv</i>, 2309.11292, doi:<a
    href="https://doi.org/10.48550/arXiv.2309.11292">10.48550/arXiv.2309.11292</a>.
  short: L. Dello Schiavo, F. Quattrocchi, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-10-28T13:13:08Z
date_published: 2023-09-20T00:00:00Z
date_updated: 2025-11-24T13:53:48Z
day: '20'
department:
- _id: GradSch
- _id: JaMa
doi: 10.48550/arXiv.2309.11292
external_id:
  arxiv:
  - '2309.11292'
keyword:
- Dirichlet distribution
- Ewens sampling formula
- Hoppe urn model
- colored partitions
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2309.11292
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
  grant_number: E208
  name: Configuration Spaces over Non-Smooth Spaces
- _id: 260482E2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: F06504
  name: Taming Complexity in Partial Differential Systems
publication: arXiv
publication_status: draft
status: public
title: Multivariate Dirichlet moments and a polychromatic Ewens sampling formula
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...