--- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '20814' abstract: - lang: eng 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. 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)." article_number: '6' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Matthias full_name: Keller, Matthias last_name: Keller - first_name: Daniel full_name: Lenz, Daniel last_name: Lenz - first_name: Marcel full_name: Schmidt, Marcel last_name: Schmidt - first_name: Michael full_name: Schwarz, Michael last_name: Schwarz - first_name: Melchior full_name: Wirth, Melchior id: 88644358-0A0E-11EA-8FA5-49A33DDC885E last_name: Wirth orcid: 0000-0002-0519-4241 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. Potential Analysis. 2026;64(1). doi:10.1007/s11118-025-10251-y apa: 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. Springer Nature. https://doi.org/10.1007/s11118-025-10251-y 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.” Potential Analysis. Springer Nature, 2026. https://doi.org/10.1007/s11118-025-10251-y. 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,” Potential Analysis, vol. 64, no. 1. Springer Nature, 2026. 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. mla: Keller, Matthias, et al. “Boundary Representations of Intermediate Forms between a Regular Dirichlet Form and Its Active Main Part.” Potential Analysis, vol. 64, no. 1, 6, Springer Nature, 2026, doi:10.1007/s11118-025-10251-y. short: M. Keller, D. Lenz, M. Schmidt, M. Schwarz, M. Wirth, Potential Analysis 64 (2026). das_tickbox: '1' dataavailabilitystatement: No datasets were generated or analysed during the current study. date_created: 2025-12-14T23:02:03Z date_published: 2026-01-01T00:00:00Z date_updated: 2026-07-27T10:25:46Z day: '01' ddc: - '510' department: - _id: JaMa doi: 10.1007/s11118-025-10251-y ec_funded: 1 external_id: arxiv: - '2301.01035' file: - access_level: open_access checksum: 9f5a4e900b8d4c74c6b5bf7c3bad54e1 content_type: application/pdf creator: dernst date_created: 2026-07-27T10:25:21Z date_updated: 2026-07-27T10:25:21Z file_id: '22414' file_name: 2026_PotentialAnalysis_Keller.pdf file_size: 445935 relation: main_file success: 1 file_date_updated: 2026-07-27T10:25:21Z fulldoi: https://doi.org/10.1007/s11118-025-10251-y has_accepted_license: '1' intvolume: ' 64' issue: '1' keyword: - Dirichlet forms - Domination of semigroups - Dirichlet - Neumann and Robin boundary conditions language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ mathsc: - 31C15 - 31C25 - 35A15 - 35J10 - 47D07 month: '01' oa: 1 oa_version: Published Version project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: 34c6ea2d-11ca-11ed-8bc3-c04f3c502833 grant_number: ESP156_N name: Gradient flow techniques for quantum Markov semigroups publication: Potential Analysis publication_identifier: eissn: - 1572-929X issn: - 0926-2601 publication_status: published publisher: Springer Nature quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Boundary representations of intermediate forms between a regular Dirichlet form and its active main part tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 64 year: '2026' ... --- OA_place: repository OA_type: green _id: '20571' abstract: - lang: eng 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. " 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" article_number: '2403.07803' article_processing_charge: No arxiv: 1 author: - first_name: Filippo full_name: Quattrocchi, Filippo id: 3ebd6ba8-edfb-11eb-afb5-91a9745ba308 last_name: Quattrocchi orcid: 0009-0000-9773-1931 citation: ama: Quattrocchi F. Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions. arXiv. doi:10.48550/arXiv.2403.07803 apa: Quattrocchi, F. (n.d.). Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions. arXiv. https://doi.org/10.48550/arXiv.2403.07803 chicago: Quattrocchi, Filippo. “Variational Structures for the Fokker-Planck Equation with General Dirichlet Boundary Conditions.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2403.07803. ieee: F. Quattrocchi, “Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions,” arXiv. . ista: Quattrocchi F. Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions. arXiv, 2403.07803. mla: Quattrocchi, Filippo. “Variational Structures for the Fokker-Planck Equation with General Dirichlet Boundary Conditions.” ArXiv, 2403.07803, doi:10.48550/arXiv.2403.07803. short: F. Quattrocchi, ArXiv (n.d.). corr_author: '1' date_created: 2025-10-28T13:12:56Z date_published: 2024-04-09T00:00:00Z date_updated: 2026-10-10T22:31:23Z day: '09' department: - _id: GradSch - _id: JaMa doi: 10.48550/arXiv.2403.07803 external_id: arxiv: - '2403.07803' fulldoi: https://doi.org/10.48550/arXiv.2403.07803 keyword: - gradient flows - Jordan–Kinderlehrer–Otto scheme - curves of maximal slope - optimal transport - Dirichlet boundary conditions - Fokker–Planck equation language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2403.07803 month: '04' oa: 1 oa_version: Preprint project: - _id: 260482E2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: F06504 name: Taming Complexity in Partial Differential Systems publication: arXiv publication_status: draft related_material: record: - id: '20865' relation: later_version status: public - id: '20563' relation: dissertation_contains status: public status: public title: Variational structures for the Fokker-Planck equation with general Dirichlet boundary conditions type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2024' ... --- 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. arXiv. doi:10.48550/arXiv.2309.11292 apa: Dello Schiavo, L., & Quattrocchi, F. (n.d.). Multivariate Dirichlet moments and a polychromatic Ewens sampling formula. arXiv. https://doi.org/10.48550/arXiv.2309.11292 chicago: Dello Schiavo, Lorenzo, and Filippo Quattrocchi. “Multivariate Dirichlet Moments and a Polychromatic Ewens Sampling Formula.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2309.11292. ieee: L. Dello Schiavo and F. Quattrocchi, “Multivariate Dirichlet moments and a polychromatic Ewens sampling formula,” arXiv. . 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.” ArXiv, 2309.11292, doi:10.48550/arXiv.2309.11292. 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' fulldoi: https://doi.org/10.48550/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' ...