[{"year":"2026","citation":{"ama":"Keller M, Lenz D, Schmidt M, Schwarz M, Wirth M. Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. <i>Potential Analysis</i>. 2026;64(1). doi:<a href=\"https://doi.org/10.1007/s11118-025-10251-y\">10.1007/s11118-025-10251-y</a>","mla":"Keller, Matthias, et al. “Boundary Representations of Intermediate Forms between a Regular Dirichlet Form and Its Active Main Part.” <i>Potential Analysis</i>, vol. 64, no. 1, 6, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s11118-025-10251-y\">10.1007/s11118-025-10251-y</a>.","chicago":"Keller, Matthias, Daniel Lenz, Marcel Schmidt, Michael Schwarz, and Melchior Wirth. “Boundary Representations of Intermediate Forms between a Regular Dirichlet Form and Its Active Main Part.” <i>Potential Analysis</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s11118-025-10251-y\">https://doi.org/10.1007/s11118-025-10251-y</a>.","short":"M. Keller, D. Lenz, M. Schmidt, M. Schwarz, M. Wirth, Potential Analysis 64 (2026).","apa":"Keller, M., Lenz, D., Schmidt, M., Schwarz, M., &#38; Wirth, M. (2026). Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. <i>Potential Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11118-025-10251-y\">https://doi.org/10.1007/s11118-025-10251-y</a>","ista":"Keller M, Lenz D, Schmidt M, Schwarz M, Wirth M. 2026. Boundary representations of intermediate forms between a regular Dirichlet form and its active main part. Potential Analysis. 64(1), 6.","ieee":"M. Keller, D. Lenz, M. Schmidt, M. Schwarz, and M. Wirth, “Boundary representations of intermediate forms between a regular Dirichlet form and its active main part,” <i>Potential Analysis</i>, vol. 64, no. 1. Springer Nature, 2026."},"PlanS_conform":"1","researchdata_availability":"no","arxiv":1,"file":[{"creator":"dernst","content_type":"application/pdf","relation":"main_file","file_size":445935,"checksum":"9f5a4e900b8d4c74c6b5bf7c3bad54e1","file_id":"22414","file_name":"2026_PotentialAnalysis_Keller.pdf","date_updated":"2026-07-27T10:25:21Z","date_created":"2026-07-27T10:25:21Z","access_level":"open_access","success":1}],"intvolume":"        64","das_tickbox":"1","ec_funded":1,"volume":64,"issue":"1","article_number":"6","_id":"20814","date_published":"2026-01-01T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"doi":"10.1007/s11118-025-10251-y","status":"public","type":"journal_article","date_updated":"2026-07-27T10:25:46Z","abstract":[{"text":"We characterize all semigroups sandwiched between the semigroup of a Dirichlet form and the semigroup of its active main part. In case the Dirichlet form is regular, we give a more explicit description of the quadratic forms of the sandwiched semigroups in terms of pairs consisting of an open set and a measure on an abstract boundary.","lang":"eng"}],"external_id":{"arxiv":["2301.01035"]},"OA_type":"hybrid","OA_place":"publisher","file_date_updated":"2026-07-27T10:25:21Z","publication_identifier":{"issn":["0926-2601"],"eissn":["1572-929X"]},"title":"Boundary representations of intermediate forms between a regular Dirichlet form and its active main part","oa":1,"has_accepted_license":"1","author":[{"first_name":"Matthias","full_name":"Keller, Matthias","last_name":"Keller"},{"last_name":"Lenz","first_name":"Daniel","full_name":"Lenz, Daniel"},{"last_name":"Schmidt","first_name":"Marcel","full_name":"Schmidt, Marcel"},{"first_name":"Michael","full_name":"Schwarz, Michael","last_name":"Schwarz"},{"last_name":"Wirth","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","first_name":"Melchior"}],"date_created":"2025-12-14T23:02:03Z","license":"https://creativecommons.org/licenses/by/4.0/","mathsc":["31C15","31C25","35A15","35J10","47D07"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (via OA deal)","keyword":["Dirichlet forms","Domination of semigroups","Dirichlet","Neumann and Robin boundary conditions"],"oa_version":"Published Version","month":"01","fulldoi":"https://doi.org/10.1007/s11118-025-10251-y","supplementarymaterial":"no","quality_controlled":"1","dataavailabilitystatement":"No datasets were generated or analysed during the current study.","publication":"Potential Analysis","ddc":["510"],"language":[{"iso":"eng"}],"article_type":"original","publication_status":"published","department":[{"_id":"JaMa"}],"publisher":"Springer Nature","day":"01","acknowledgement":"Open Access funding enabled and organized by Projekt DEAL. The first three authors acknowledge financial support of the DFG within the priority programme Geometry at Infinity.\r\nM.W. acknowledges financial support by the German Academic Scholarship Foundation, by the Austrian Science Fund (FWF) through grant number F65 and the Esprit Programme [ESP 156], and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117).","project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","call_identifier":"H2020"},{"_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","name":"Gradient flow techniques for quantum Markov semigroups","grant_number":"ESP156_N"}],"scopus_import":"1"},{"keyword":["gradient flows","Jordan–Kinderlehrer–Otto scheme","curves of maximal slope","optimal transport","Dirichlet boundary conditions","Fokker–Planck equation"],"article_processing_charge":"No","oa_version":"Preprint","fulldoi":"https://doi.org/10.48550/arXiv.2403.07803","month":"04","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","date_created":"2025-10-28T13:12:56Z","author":[{"orcid":"0009-0000-9773-1931","last_name":"Quattrocchi","id":"3ebd6ba8-edfb-11eb-afb5-91a9745ba308","full_name":"Quattrocchi, Filippo","first_name":"Filippo"}],"acknowledgement":"The author would like to thank Jan Maas for suggesting this project and for many helpful\r\ncomments, Antonio Agresti, Lorenzo Dello Schiavo and Julian Fischer for several fruitful discussions, and Oliver Tse for pointing out the reference [15]. He also gratefully acknowledges support from the Austrian Science Fund (FWF) project 10.55776/F65.\r\n","project":[{"grant_number":"F06504","call_identifier":"FWF","_id":"260482E2-B435-11E9-9278-68D0E5697425","name":"Taming Complexity in Partial Differential Systems"}],"department":[{"_id":"GradSch"},{"_id":"JaMa"}],"day":"09","language":[{"iso":"eng"}],"publication_status":"draft","publication":"arXiv","citation":{"chicago":"Quattrocchi, Filippo. “Variational Structures for the Fokker-Planck Equation with General Dirichlet Boundary Conditions.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2403.07803\">https://doi.org/10.48550/arXiv.2403.07803</a>.","mla":"Quattrocchi, Filippo. “Variational Structures for the Fokker-Planck Equation with General Dirichlet Boundary Conditions.” <i>ArXiv</i>, 2403.07803, doi:<a href=\"https://doi.org/10.48550/arXiv.2403.07803\">10.48550/arXiv.2403.07803</a>.","ama":"Quattrocchi F. Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2403.07803\">10.48550/arXiv.2403.07803</a>","ista":"Quattrocchi F. Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions. arXiv, 2403.07803.","ieee":"F. Quattrocchi, “Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions,” <i>arXiv</i>. .","apa":"Quattrocchi, F. (n.d.). Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2403.07803\">https://doi.org/10.48550/arXiv.2403.07803</a>","short":"F. Quattrocchi, ArXiv (n.d.)."},"arxiv":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2403.07803","open_access":"1"}],"year":"2024","OA_type":"green","OA_place":"repository","title":"Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions","oa":1,"abstract":[{"text":"We prove the convergence of a modified Jordan--Kinderlehrer--Otto scheme to a solution to the Fokker--Planck equation in $\\Omega \\Subset \\mathbb{R}^d$ with general, positive and temporally constant, Dirichlet boundary conditions. We work under mild assumptions on the domain, the drift, and the initial datum.   In the special case where $\\Omega$ is an interval in $\\mathbb{R}^1$, we prove that such a solution is a gradient flow -- curve of maximal slope -- within a suitable space of measures, endowed with a modified Wasserstein distance.\r\nOur discrete scheme and modified distance draw inspiration from contributions by A. Figalli and N. Gigli [J. Math. Pures Appl. 94, (2010), pp. 107--130], and J. Morales [J. Math. Pures Appl. 112, (2018), pp. 41--88] on an optimal-transport approach to evolution equations with Dirichlet boundary conditions. Similarly to these works, we allow the mass to flow from/to the boundary $\\partial \\Omega$ throughout the evolution. However, our leading idea is to also keep track of the mass at the boundary by working with measures defined on the whole closure $\\overline \\Omega$. The driving functional is a modification of the classical relative entropy that also makes use of the information at the boundary. As an intermediate result, when $\\Omega$ is an interval in $\\mathbb{R}^1$, we find a formula for the descending slope of this geodesically nonconvex functional. ","lang":"eng"}],"external_id":{"arxiv":["2403.07803"]},"_id":"20571","date_published":"2024-04-09T00:00:00Z","doi":"10.48550/arXiv.2403.07803","status":"public","type":"preprint","related_material":{"record":[{"status":"public","id":"20865","relation":"later_version"},{"status":"public","id":"20563","relation":"dissertation_contains"}]},"date_updated":"2026-10-10T22:31:23Z","article_number":"2403.07803"},{"external_id":{"arxiv":["2309.11292"]},"abstract":[{"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.","lang":"eng"}],"oa":1,"title":"Multivariate Dirichlet moments and a polychromatic Ewens sampling formula","OA_place":"repository","OA_type":"green","article_number":"2309.11292","date_updated":"2025-11-24T13:53:48Z","type":"preprint","status":"public","doi":"10.48550/arXiv.2309.11292","date_published":"2023-09-20T00:00:00Z","_id":"20572","arxiv":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2309.11292","open_access":"1"}],"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>","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>.","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>.","short":"L. Dello Schiavo, F. Quattrocchi, ArXiv (n.d.).","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.","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>"},"year":"2023","day":"20","department":[{"_id":"GradSch"},{"_id":"JaMa"}],"project":[{"grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c"},{"name":"Taming Complexity in Partial Differential Systems","_id":"260482E2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"F06504"}],"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.","publication":"arXiv","publication_status":"draft","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","fulldoi":"https://doi.org/10.48550/arXiv.2309.11292","month":"09","oa_version":"Preprint","article_processing_charge":"No","keyword":["Dirichlet distribution","Ewens sampling formula","Hoppe urn model","colored partitions"],"author":[{"first_name":"Lorenzo","full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"},{"full_name":"Quattrocchi, Filippo","first_name":"Filippo","last_name":"Quattrocchi","id":"3ebd6ba8-edfb-11eb-afb5-91a9745ba308","orcid":"0009-0000-9773-1931"}],"date_created":"2025-10-28T13:13:08Z","corr_author":"1"}]