2026-04-05T10:44:30Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/3775812024-12-20T14:14:55Zcom_2072_199267com_2072_4427col_2072_199862

Optimal transportation of processes with infinite Kantorovich distance. Independence and symmetry Kolesnikov, A.V. Zaev, D.A. We consider probability measures on $ \mathbb{R}^{\infty}$ and study natural \linebreak analogs of optimal transportation mappings for the case of infinite Kantorovich distance. Our examples include 1) quasi-product measures, 2) measures with certain symmetric properties, in particular, exchangeable and stationary measures. It turns out that the existence problem for optimal transportation is closely related to various ergodic properties. We prove the existence of optimal transportation for a certain class of stationary Gibbs measures. In addition, we establish a variant of the Kantorovich duality for the Monge--Kantorovich problem restricted to the case of measures invariant with respect of actions of compact groups. 2020-10-14T13:20:43Z 2024-09-19T13:36:03Z 2020-10-14T13:20:43Z 2024-09-19T13:36:03Z 2014-01-01 info:eu-repo/semantics/preprint http://hdl.handle.net/2072/377581 eng CRM Preprints info:eu-repo/semantics/openAccess L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons:http://creativecommons.org/licenses/by-nc-nd/4.0/ RECERCAT (Dipòsit de la Recerca de Catalunya)