{"status":"public","title":"Isometric study of Wasserstein spaces - the real line","quality_controlled":"1","date_created":"2020-01-29T10:20:46Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"oa_version":"Preprint","publisher":"American Mathematical Society","issue":"8","date_published":"2020-08-01T00:00:00Z","publication_status":"published","abstract":[{"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)).","lang":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/2002.00859","open_access":"1"}],"department":[{"_id":"LaEr"}],"day":"01","type":"journal_article","date_updated":"2023-08-17T14:31:03Z","article_processing_charge":"No","month":"08","keyword":["Wasserstein space","isometric embeddings","isometric rigidity","exotic isometry flow"],"isi":1,"ddc":["515"],"project":[{"grant_number":"846294","_id":"26A455A6-B435-11E9-9278-68D0E5697425","name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020"}],"volume":373,"intvolume":"       373","year":"2020","ec_funded":1,"article_type":"original","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>.","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.","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>","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.","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>","short":"G.P. Geher, T. Titkos, D. Virosztek, Transactions of the American Mathematical Society 373 (2020) 5855–5883."},"language":[{"iso":"eng"}],"_id":"7389","page":"5855-5883","doi":"10.1090/tran/8113","publication":"Transactions of the American Mathematical Society","author":[{"last_name":"Geher","first_name":"Gyorgy Pal","full_name":"Geher, Gyorgy Pal"},{"full_name":"Titkos, Tamas","last_name":"Titkos","first_name":"Tamas"},{"first_name":"Daniel","last_name":"Virosztek","full_name":"Virosztek, Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1109-5511"}],"publication_identifier":{"issn":["00029947"],"eissn":["10886850"]},"external_id":{"arxiv":["2002.00859"],"isi":["000551418100018"]}}