[{"language":[{"iso":"eng"}],"publication":"Transactions of the American Mathematical Society","title":"Isometric study of Wasserstein spaces - the real line","oa":1,"date_updated":"2023-08-17T14:31:03Z","article_processing_charge":"No","issue":"8","intvolume":"       373","isi":1,"status":"public","type":"journal_article","author":[{"full_name":"Geher, Gyorgy Pal","first_name":"Gyorgy Pal","last_name":"Geher"},{"last_name":"Titkos","first_name":"Tamas","full_name":"Titkos, Tamas"},{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","last_name":"Virosztek","orcid":"0000-0003-1109-5511","first_name":"Daniel","full_name":"Virosztek, Daniel"}],"arxiv":1,"oa_version":"Preprint","day":"01","main_file_link":[{"url":"https://arxiv.org/abs/2002.00859","open_access":"1"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"eissn":["10886850"],"issn":["00029947"]},"month":"08","_id":"7389","article_type":"original","doi":"10.1090/tran/8113","date_created":"2020-01-29T10:20:46Z","citation":{"mla":"Geher, Gyorgy Pal, et al. “Isometric Study of Wasserstein Spaces - the Real Line.” <i>Transactions of the American Mathematical Society</i>, vol. 373, no. 8, American Mathematical Society, 2020, pp. 5855–83, doi:<a href=\"https://doi.org/10.1090/tran/8113\">10.1090/tran/8113</a>.","chicago":"Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Isometric Study of Wasserstein Spaces - the Real Line.” <i>Transactions of the American Mathematical Society</i>. American Mathematical Society, 2020. <a href=\"https://doi.org/10.1090/tran/8113\">https://doi.org/10.1090/tran/8113</a>.","ista":"Geher GP, Titkos T, Virosztek D. 2020. Isometric study of Wasserstein spaces - the real line. Transactions of the American Mathematical Society. 373(8), 5855–5883.","short":"G.P. Geher, T. Titkos, D. Virosztek, Transactions of the American Mathematical Society 373 (2020) 5855–5883.","ama":"Geher GP, Titkos T, Virosztek D. Isometric study of Wasserstein spaces - the real line. <i>Transactions of the American Mathematical Society</i>. 2020;373(8):5855-5883. doi:<a href=\"https://doi.org/10.1090/tran/8113\">10.1090/tran/8113</a>","ieee":"G. P. Geher, T. Titkos, and D. Virosztek, “Isometric study of Wasserstein spaces - the real line,” <i>Transactions of the American Mathematical Society</i>, vol. 373, no. 8. American Mathematical Society, pp. 5855–5883, 2020.","apa":"Geher, G. P., Titkos, T., &#38; Virosztek, D. (2020). Isometric study of Wasserstein spaces - the real line. <i>Transactions of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/tran/8113\">https://doi.org/10.1090/tran/8113</a>"},"keyword":["Wasserstein space","isometric embeddings","isometric rigidity","exotic isometry flow"],"year":"2020","ec_funded":1,"project":[{"call_identifier":"H2020","name":"Geometric study of Wasserstein spaces and free probability","grant_number":"846294","_id":"26A455A6-B435-11E9-9278-68D0E5697425"}],"page":"5855-5883","department":[{"_id":"LaEr"}],"volume":373,"quality_controlled":"1","publisher":"American Mathematical Society","date_published":"2020-08-01T00:00:00Z","publication_status":"published","external_id":{"arxiv":["2002.00859"],"isi":["000551418100018"]},"abstract":[{"lang":"eng","text":"Recently Kloeckner described the structure of the isometry group of the quadratic Wasserstein space W_2(R^n). It turned out that the case of the real line is exceptional in the sense that there exists an exotic isometry flow. Following this line of investigation, we compute Isom(W_p(R)), the isometry group of the Wasserstein space\r\nW_p(R) for all p \\in [1,\\infty) \\setminus {2}. We show that W_2(R) is also exceptional regarding the\r\nparameter p: W_p(R) is isometrically rigid if and only if p is not equal to 2. Regarding the underlying\r\nspace, we prove that the exceptionality of p = 2 disappears if we replace R by the compact\r\ninterval [0,1]. Surprisingly, in that case, W_p([0,1]) is isometrically rigid if and only if\r\np is not equal to 1. Moreover, W_1([0,1]) admits isometries that split mass, and Isom(W_1([0,1]))\r\ncannot be embedded into Isom(W_1(R))."}],"ddc":["515"]}]