{"year":"2023","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2309.11292"}],"date_updated":"2025-11-24T13:53:48Z","oa_version":"Preprint","keyword":["Dirichlet distribution","Ewens sampling formula","Hoppe urn model","colored partitions"],"date_published":"2023-09-20T00:00:00Z","OA_place":"repository","external_id":{"arxiv":["2309.11292"]},"month":"09","type":"preprint","publication_status":"draft","_id":"20572","article_processing_charge":"No","doi":"10.48550/arXiv.2309.11292","date_created":"2025-10-28T13:13:08Z","language":[{"iso":"eng"}],"OA_type":"green","project":[{"name":"Configuration Spaces over Non-Smooth Spaces","grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c"},{"call_identifier":"FWF","_id":"260482E2-B435-11E9-9278-68D0E5697425","grant_number":"F06504","name":"Taming Complexity in Partial Differential Systems"}],"arxiv":1,"status":"public","corr_author":"1","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."}],"department":[{"_id":"GradSch"},{"_id":"JaMa"}],"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.","citation":{"short":"L. Dello Schiavo, F. Quattrocchi, ArXiv (n.d.).","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>.","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>","ista":"Dello Schiavo L, Quattrocchi F. Multivariate Dirichlet moments and a polychromatic Ewens sampling formula. arXiv, 2309.11292.","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>","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>.","ieee":"L. Dello Schiavo and F. Quattrocchi, “Multivariate Dirichlet moments and a polychromatic Ewens sampling formula,” <i>arXiv</i>. ."},"article_number":"2309.11292","author":[{"full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","first_name":"Lorenzo","orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"},{"id":"3ebd6ba8-edfb-11eb-afb5-91a9745ba308","orcid":"0009-0000-9773-1931","first_name":"Filippo","full_name":"Quattrocchi, Filippo","last_name":"Quattrocchi"}],"day":"20","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Multivariate Dirichlet moments and a polychromatic Ewens sampling formula","publication":"arXiv","oa":1}