[{"oa_version":"Preprint","publisher":"American Mathematical Society","title":"Isometric study of Wasserstein spaces - the real line","main_file_link":[{"url":"https://arxiv.org/abs/2002.00859","open_access":"1"}],"ddc":["515"],"publication_identifier":{"eissn":["10886850"],"issn":["00029947"]},"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))."}],"date_created":"2020-01-29T10:20:46Z","_id":"7389","intvolume":" 373","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Transactions of the American Mathematical Society","citation":{"ama":"Geher GP, Titkos T, Virosztek D. Isometric study of Wasserstein spaces - the real line. *Transactions of the American Mathematical Society*. 2020;373(8):5855-5883. doi:10.1090/tran/8113","apa":"Geher, G. P., Titkos, T., & Virosztek, D. (2020). Isometric study of Wasserstein spaces - the real line. *Transactions of the American Mathematical Society*, *373*(8), 5855–5883. https://doi.org/10.1090/tran/8113","mla":"Geher, Gyorgy Pal, et al. “Isometric Study of Wasserstein Spaces - the Real Line.” *Transactions of the American Mathematical Society*, vol. 373, no. 8, American Mathematical Society, 2020, pp. 5855–83, doi:10.1090/tran/8113.","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.","ieee":"G. P. Geher, T. Titkos, and D. Virosztek, “Isometric study of Wasserstein spaces - the real line,” *Transactions of the American Mathematical Society*, vol. 373, no. 8, pp. 5855–5883, 2020.","chicago":"Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Isometric Study of Wasserstein Spaces - the Real Line.” *Transactions of the American Mathematical Society* 373, no. 8 (2020): 5855–83. https://doi.org/10.1090/tran/8113."},"year":"2020","department":[{"_id":"LaEr"}],"status":"public","article_type":"original","external_id":{"arxiv":["2002.00859"]},"day":"01","oa":1,"date_updated":"2020-07-27T14:41:06Z","month":"08","project":[{"grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425"}],"publication_status":"published","type":"journal_article","author":[{"full_name":"Geher, Gyorgy Pal","last_name":"Geher","first_name":"Gyorgy Pal"},{"last_name":"Titkos","full_name":"Titkos, Tamas","first_name":"Tamas"},{"last_name":"Virosztek","full_name":"Virosztek, Daniel","first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"language":[{"iso":"eng"}],"volume":373,"issue":"8","doi":"10.1090/tran/8113","page":"5855-5883","keyword":["Wasserstein space","isometric embeddings","isometric rigidity","exotic isometry flow"],"article_processing_charge":"No","date_published":"2020-08-01T00:00:00Z"}]