{"publication":"Journal of the London Mathematical Society","doi":"10.1112/jlms.12676","ec_funded":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2102.02037"}],"article_type":"original","publication_identifier":{"eissn":["1469-7750"],"issn":["0024-6107"]},"intvolume":"       106","date_updated":"2023-08-04T09:24:17Z","day":"18","year":"2022","language":[{"iso":"eng"}],"oa":1,"external_id":{"isi":["000854878500001"],"arxiv":["2102.02037"]},"abstract":[{"lang":"eng","text":"Motivated by Kloeckner’s result on the isometry group of the quadratic Wasserstein space W2(Rn), we describe the isometry group Isom(Wp(E)) for all parameters 0 < p < ∞ and for all separable real Hilbert spaces E. In particular, we show that Wp(X) is isometrically rigid for all Polish space X whenever 0 < p < 1. This is a consequence of our more general result: we prove that W1(X) is isometrically rigid if X is a complete separable metric space that satisfies the strict triangle inequality. Furthermore, we show that this latter rigidity result does not generalise to parameters p > 1, by solving Kloeckner’s problem affirmatively on the existence of mass-splitting isometries. "}],"publisher":"Wiley","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"page":"3865-3894","oa_version":"Preprint","keyword":["General Mathematics"],"type":"journal_article","article_processing_charge":"No","department":[{"_id":"LaEr"}],"issue":"4","publication_status":"published","quality_controlled":"1","volume":106,"status":"public","_id":"12214","month":"09","author":[{"full_name":"Gehér, György Pál","first_name":"György Pál","last_name":"Gehér"},{"first_name":"Tamás","last_name":"Titkos","full_name":"Titkos, Tamás"},{"orcid":"0000-0003-1109-5511","last_name":"Virosztek","first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","full_name":"Virosztek, Daniel"}],"citation":{"short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of the London Mathematical Society 106 (2022) 3865–3894.","apa":"Gehér, G. P., Titkos, T., &#38; Virosztek, D. (2022). The isometry group of Wasserstein spaces: The Hilbertian case. <i>Journal of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/jlms.12676\">https://doi.org/10.1112/jlms.12676</a>","mla":"Gehér, György Pál, et al. “The Isometry Group of Wasserstein Spaces: The Hilbertian Case.” <i>Journal of the London Mathematical Society</i>, vol. 106, no. 4, Wiley, 2022, pp. 3865–94, doi:<a href=\"https://doi.org/10.1112/jlms.12676\">10.1112/jlms.12676</a>.","ista":"Gehér GP, Titkos T, Virosztek D. 2022. The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. 106(4), 3865–3894.","ieee":"G. P. Gehér, T. Titkos, and D. Virosztek, “The isometry group of Wasserstein spaces: The Hilbertian case,” <i>Journal of the London Mathematical Society</i>, vol. 106, no. 4. Wiley, pp. 3865–3894, 2022.","ama":"Gehér GP, Titkos T, Virosztek D. The isometry group of Wasserstein spaces: The Hilbertian case. <i>Journal of the London Mathematical Society</i>. 2022;106(4):3865-3894. doi:<a href=\"https://doi.org/10.1112/jlms.12676\">10.1112/jlms.12676</a>","chicago":"Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “The Isometry Group of Wasserstein Spaces: The Hilbertian Case.” <i>Journal of the London Mathematical Society</i>. Wiley, 2022. <a href=\"https://doi.org/10.1112/jlms.12676\">https://doi.org/10.1112/jlms.12676</a>."},"acknowledgement":"Geher was supported by the Leverhulme Trust Early Career Fellowship (ECF-2018-125), and also by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. K115383 and K134944).\r\nTitkos was supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. PD128374, grant no. K115383 and K134944), by the J´anos Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the UNKP-20-5-BGE-1 New National Excellence Program of the ´Ministry of Innovation and Technology.\r\nVirosztek was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, by the Momentum program of the Hungarian Academy of Sciences under grant agreement no. LP2021-15/2021, and partially supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grants no. K124152 and no. KH129601). ","date_created":"2023-01-16T09:46:13Z","scopus_import":"1","title":"The isometry group of Wasserstein spaces: The Hilbertian case","project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","grant_number":"846294","call_identifier":"H2020","name":"Geometric study of Wasserstein spaces and free probability"}],"date_published":"2022-09-18T00:00:00Z"}