[{"oa":1,"keyword":["Wasserstein space","isometric embeddings","isometric rigidity","exotic isometry flow"],"year":"2020","date_updated":"2023-08-17T14:31:03Z","publication":"Transactions of the American Mathematical Society","article_type":"original","page":"5855-5883","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"LaEr"}],"date_created":"2020-01-29T10:20:46Z","external_id":{"isi":["000551418100018"],"arxiv":["2002.00859"]},"date_published":"2020-08-01T00:00:00Z","intvolume":"       373","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2002.00859"}],"publisher":"American Mathematical Society","language":[{"iso":"eng"}],"quality_controlled":"1","type":"journal_article","isi":1,"_id":"7389","author":[{"last_name":"Geher","full_name":"Geher, Gyorgy Pal","first_name":"Gyorgy Pal"},{"full_name":"Titkos, Tamas","last_name":"Titkos","first_name":"Tamas"},{"last_name":"Virosztek","full_name":"Virosztek, Daniel","first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1109-5511"}],"title":"Isometric study of Wasserstein spaces - the real line","doi":"10.1090/tran/8113","issue":"8","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"}],"project":[{"grant_number":"846294","_id":"26A455A6-B435-11E9-9278-68D0E5697425","name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020"}],"publication_identifier":{"issn":["00029947"],"eissn":["10886850"]},"ec_funded":1,"publication_status":"published","status":"public","month":"08","ddc":["515"],"day":"01","citation":{"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>","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>","short":"G.P. Geher, T. Titkos, D. Virosztek, Transactions of the American Mathematical Society 373 (2020) 5855–5883.","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.","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>."},"oa_version":"Preprint","arxiv":1,"article_processing_charge":"No","volume":373},{"page":"5757-5785","publication":"Transactions of the American Mathematical Society","date_updated":"2023-08-24T14:34:56Z","year":"2019","oa":1,"isi":1,"quality_controlled":"1","type":"journal_article","language":[{"iso":"eng"}],"publisher":"American Mathematical Society","main_file_link":[{"url":"https://arxiv.org/abs/1705.01999","open_access":"1"}],"intvolume":"       371","external_id":{"isi":["000464034200019"],"arxiv":["1705.01999"]},"date_published":"2019-04-15T00:00:00Z","date_created":"2018-12-11T11:45:01Z","scopus_import":"1","department":[{"_id":"TiBr"}],"publist_id":"7746","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","publication_status":"published","publication_identifier":{"issn":["00029947"],"eissn":["10886850"]},"abstract":[{"text":"An upper bound sieve for rational points on suitable varieties isdeveloped, together with applications tocounting rational points in thin sets,to local solubility in families, and to the notion of “friable” rational pointswith respect to divisors. In the special case of quadrics, sharper estimates areobtained by developing a version of the Selberg sieve for rational points.","lang":"eng"}],"issue":"8","doi":"10.1090/tran/7514","title":"Sieving rational points on varieties","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","full_name":"Browning, Timothy D","last_name":"Browning","orcid":"0000-0002-8314-0177"},{"first_name":"Daniel","last_name":"Loughran","full_name":"Loughran, Daniel"}],"_id":"175","article_processing_charge":"No","volume":371,"arxiv":1,"oa_version":"Preprint","citation":{"mla":"Browning, Timothy D., and Daniel Loughran. “Sieving Rational Points on Varieties.” <i>Transactions of the American Mathematical Society</i>, vol. 371, no. 8, American Mathematical Society, 2019, pp. 5757–85, doi:<a href=\"https://doi.org/10.1090/tran/7514\">10.1090/tran/7514</a>.","chicago":"Browning, Timothy D, and Daniel Loughran. “Sieving Rational Points on Varieties.” <i>Transactions of the American Mathematical Society</i>. American Mathematical Society, 2019. <a href=\"https://doi.org/10.1090/tran/7514\">https://doi.org/10.1090/tran/7514</a>.","apa":"Browning, T. D., &#38; Loughran, D. (2019). Sieving rational points on varieties. <i>Transactions of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/tran/7514\">https://doi.org/10.1090/tran/7514</a>","ieee":"T. D. Browning and D. Loughran, “Sieving rational points on varieties,” <i>Transactions of the American Mathematical Society</i>, vol. 371, no. 8. American Mathematical Society, pp. 5757–5785, 2019.","ista":"Browning TD, Loughran D. 2019. Sieving rational points on varieties. Transactions of the American Mathematical Society. 371(8), 5757–5785.","short":"T.D. Browning, D. Loughran, Transactions of the American Mathematical Society 371 (2019) 5757–5785.","ama":"Browning TD, Loughran D. Sieving rational points on varieties. <i>Transactions of the American Mathematical Society</i>. 2019;371(8):5757-5785. doi:<a href=\"https://doi.org/10.1090/tran/7514\">10.1090/tran/7514</a>"},"day":"15","month":"04"}]