Isometric study of Wasserstein spaces - the real line

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.


Journal Article | Published | English
Author
Geher, Gyorgy Pal; Titkos, Tamas; Virosztek, DanielIST Austria
Department
Abstract
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 W_p(R) for all p \in [1,\infty) \setminus {2}. We show that W_2(R) is also exceptional regarding the parameter p: W_p(R) is isometrically rigid if and only if p is not equal to 2. Regarding the underlying space, we prove that the exceptionality of p = 2 disappears if we replace R by the compact interval [0,1]. Surprisingly, in that case, W_p([0,1]) is isometrically rigid if and only if p is not equal to 1. Moreover, W_1([0,1]) admits isometries that split mass, and Isom(W_1([0,1])) cannot be embedded into Isom(W_1(R)).
Publishing Year
Date Published
2020-08-01
Journal Title
Transactions of the American Mathematical Society
Volume
373
Issue
8
Page
5855-5883
ISSN
eISSN
IST-REx-ID

Cite this

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
Geher, G. P., Titkos, T., & Virosztek, D. (2020). Isometric study of Wasserstein spaces - the real line. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/8113
Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Isometric Study of Wasserstein Spaces - the Real Line.” Transactions of the American Mathematical Society. American Mathematical Society, 2020. https://doi.org/10.1090/tran/8113.
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. American Mathematical Society, pp. 5855–5883, 2020.
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.
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.
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arXiv 2002.00859

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