Fetching the paper…
Reading the bibliography…
We prove that the sequence of marginals obtained from the iterations of the Sinkhorn algorithm or the iterative proportional fitting procedure (IPFP) on joint densities, converges to an absolutely continuous curve on the $2$-Wasserstein space, as the regularization parameter $\varepsilon$ goes to zero and the number of iterations is scaled as $1/\varepsilon$ (and other technical assumptions).
1905
Earlier work this paper cites.
Henry P McKean Jr,
1911
Earlier work this paper cites.
Christian Léonard,
1920
Earlier work this paper cites.
E. Schrödinger,
1932
Earlier work this paper cites.
L. Kantorovitch,
1942
Earlier work this paper cites.
Mark Kac,
1956
Earlier work this paper cites.
Richard Sinkhorn,
1967
Earlier work this paper cites.
Imre Csiszár,
1975
Earlier work this paper cites.
H. P. McKean,
1975
Earlier work this paper cites.
H. Tanaka,
1978
Earlier work this paper cites.
L. Dobrushin, R.,
1979
Earlier work this paper cites.
A.S. Nemirovsky, D.B. Yudin, and E.R. Dawson,
1983
Earlier work this paper cites.
D. Bakry and Michel Émery,
1985
Earlier work this paper cites.
Richard Holley and Daniel Stroock,
1987
Earlier work this paper cites.
Joel Franklin and Jens Lorenz,
1989
Earlier work this paper cites.
Ioannis Karatzas and Steven E. Shreve,
1991
Earlier work this paper cites.
Alain-Sol Sznitman,
1991
Earlier work this paper cites.
R. Cominetti and J. San Martín,
1994
Earlier work this paper cites.
Roger A Horn and Charles R Johnson,
1994
Earlier work this paper cites.
Robert J. McCann,
1995
Earlier work this paper cites.
Ludger Rüschendorf,
1995
Earlier work this paper cites.
Gareth O Roberts and Richard L Tweedie,
1996
Earlier work this paper cites.
Shima Hirohiko and Katsumi Yagi,
1997
Earlier work this paper cites.
Don S Lemons and Anthony Gythiel,
1997
Earlier work this paper cites.
Richard Jordan, David Kinderlehrer, and Felix Otto,
1998
Earlier work this paper cites.
Beatrice Laurent and Pascal Massart,
2000
Earlier work this paper cites.
F. Otto and C. Villani,
2000
Earlier work this paper cites.
Yossi Rubner, Carlo Tomasi, and Leonidas J Guibas,
2000
Earlier work this paper cites.
Anton Arnold, Peter Markowich, Giuseppe Toscani, and Andreas Unterreiter,
2001
Earlier work this paper cites.
Robert McCann,
2001
Cited alongside, same era.
Felix Otto,
2001
Cited alongside, same era.
Feng-Yu Wang,
2001
Cited alongside, same era.
Cédric Villani,
2003
Cited alongside, same era.
Stephen P Boyd and Lieven Vandenberghe,
2004
Cited alongside, same era.
Toshio Mikami,
2004
Cited alongside, same era.
Luigi Ambrosio, Nicola Gigli, and Giuseppe Savaré,
2008
Cited alongside, same era.
Philip A Knight,
2008
Robert J Berman,
2020
Later among the works it cites.
Tianji Cai, Junyi Cheng, Nathaniel Craig, and Katy Craig,
2020
Later among the works it cites.
Guillaume Carlier and Maxime Laborde,
2020
Later among the works it cites.
Sinho Chewi, Thibaut Le Gouic, Chen Lu, Tyler Maunu, Philippe Rigollet, and Austin Stromme,
2020
Later among the works it cites.
Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole,
2020
Later among the works it cites.
2020
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Patrick Cattiaux, Arnaud Guillin, and Li-Ming Wu,
2010
Cited alongside, same era.
Jun Kitagawa,
2012
Cited alongside, same era.
Alexander V. Kolesnikov,
2012
Cited alongside, same era.
Young-Heon Kim, Jeffrey Streets, and Micah Warren,
2012
Cited alongside, same era.
Kelvin Shuangjian Zhang, Gabriel Peyré, Jalal Fadili, and Marcelo Pereyra,
2020
Later among the works it cites.
Kwangjun Ahn and Sinho Chewi,
2021
Later among the works it cites.
Hong-Bin Chen, Sinho Chewi, and Jonathan Niles-Weed,
2021
Later among the works it cites.
Giovanni Conforti and Luca Tamanini,
2021
Later among the works it cites.
George Deligiannidis, Valentin De Bortoli, and Arnaud Doucet,
2021
Later among the works it cites.
Flavien Léger,
2021
Later among the works it cites.
Espen Bernton, Promit Ghosal, and Marcel Nutz,
2022
Later among the works it cites.
Alberto Chiarini, Giovanni Conforti, Giacomo Greco, and Luca Tamanini,
2022
Later among the works it cites.
Louis-Pierre Chaintron and Antoine Diez,
2022
Later among the works it cites.
Guillaume Carlier, Paul Pegon, and Luca Tamanini,
2022
Later among the works it cites.
Lénaïc Chizat, Stephen Zhang, Matthieu Heitz, and Geoffrey Schiebinger,
2022
Later among the works it cites.
Stephan Eckstein and Marcel Nutz,
2022
Later among the works it cites.
by same author,
2022
Later among the works it cites.
Promit Ghosal and Marcel Nutz,
2022
Later among the works it cites.
Promit Ghosal, Marcel Nutz, and Espen Bernton,
2022
Later among the works it cites.
Marcel Nutz and Johannes Wiesel,
2022
Later among the works it cites.
R. Bhattacharya and E.C. Waymire,
2023
Closest in time.
Caroline Moosmüller and Alexander Cloninger,
2023
Closest in time.
by same author,
2023
Closest in time.
2023
Closest in time.
Louis Sharrock, Lester Mackey, and Christopher Nemeth,
2023
Closest in time.
2024
Closest in time.
Nabarun Deb and Tengyuan Liang,
2025
Closest in time.