{"issue":"4","publisher":"Wiley","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. "}],"year":"2022","publication_identifier":{"issn":["0024-6107"],"eissn":["1469-7750"]},"oa_version":"Preprint","department":[{"_id":"LaEr"}],"ec_funded":1,"status":"public","article_type":"original","date_created":"2023-01-16T09:46:13Z","citation":{"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>.","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>","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>","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.","short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of the London Mathematical Society 106 (2022) 3865–3894.","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.","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>."},"type":"journal_article","month":"09","date_updated":"2023-08-04T09:24:17Z","title":"The isometry group of Wasserstein spaces: The Hilbertian case","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). ","article_processing_charge":"No","keyword":["General Mathematics"],"isi":1,"scopus_import":"1","intvolume":"       106","language":[{"iso":"eng"}],"quality_controlled":"1","oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2102.02037","open_access":"1"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","page":"3865-3894","date_published":"2022-09-18T00:00:00Z","publication_status":"published","day":"18","publication":"Journal of the London Mathematical Society","author":[{"first_name":"György Pál","last_name":"Gehér","full_name":"Gehér, György Pál"},{"first_name":"Tamás","last_name":"Titkos","full_name":"Titkos, Tamás"},{"full_name":"Virosztek, Daniel","last_name":"Virosztek","orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel"}],"doi":"10.1112/jlms.12676","_id":"12214","volume":106,"external_id":{"isi":["000854878500001"],"arxiv":["2102.02037"]},"project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","name":"Geometric study of Wasserstein spaces and free probability","grant_number":"846294","call_identifier":"H2020"}]}