• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Preprints
  • Optimal transportation of processes with infinite Kantorovich distance. Independence and symmetry.
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
July 9, 2026
HSE Economists Use Search Queries to Forecast Birth Rates
Researchers from the HSE Faculty of Economic Sciences have shown that the accuracy of birth rate forecasts for Russia can be improved by almost 50% by incorporating the dynamics of online search queries related to pregnancy and childbirth into forecasting models. In the best-performing models, the forecasting error fell from 4.6% to 3.2%. The findings have been published in Populations and Economics.
July 8, 2026
HSE Researchers Discover Who Eats Out in Russia-And Why
Around one-third of Russians (31.3%) rarely eat out or buy ready-made meals. The core group of active consumers—those who eat out or purchase prepared food almost every day or several times a week—accounts for only about 9% of the population. These are the findings of a study conducted by the HSE Institute for Social Policy. According to the researchers eating out is no longer a marker of high social status in Russia.
July 8, 2026
HSE University and RREDA Join Forces to Support 2026 Renewable Energy of the Planet Competition
HSE University and the Russia Renewable Energy Development Association (RREDA) have signed a partnership and information cooperation agreement to support Renewable Energy of the Planet—2026, a national competition with international participation for students and early-career researchers. Applications are open on the competition's website until September 20, 2026.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Optimal transportation of processes with infinite Kantorovich distance. Independence and symmetry.

2013.
Kolesnikov A., Zaev D.
We consider probability measures on $\mathbb{R}^{\infty}$ and study natural 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.
Research target: Mathematics
Language: English
Full text
Text on another site
Keywords: Optimal transportationMonge-Kantorovich problemGibbs measuresGaussian measuresstationary measuresergodic measuresKantorovich dualitylinear programming
Publication based on the results of:
Вариационные и геометрические задачи анализа (2014)
Similar publications
Statistical inference based on band-limited kernels: Rational-infinitely divisible distributions and beyond
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Computational Science and Its Applications – ICCSA 2026 Workshops
Springer, 2027.
The series Lecture Notes in Computer Science (LNCS), including its subseries Lecture Notes in Artificial Intelligence (LNAI) and Lecture Notes in Bioinformatics (LNBI), has established itself as a medium for the publication of new developments in computer science and information technology research, teaching, and education. LNCS enjoys close cooperation with the computer science R & ...
Added: July 8, 2026
Моделирование специализированных алгоритмов маршрутизации в сетях на кристалле, представленных сериями семейств циркулянтных топологий
Маликов М. А., Монахова Э. А., Rzaev E. et al., Ученые записки Казанского университета. Серия: Физико-математические науки 2026 Т. 168 № 2 С. 269–286
This article examines series of families of two-dimensional circulant networks with rectangular L -shapes, optimal in diameter, as network-on-chip topologies with a minimal number of crossings between the links and a bounded length of the maximum link that does not depend on the network size. New network-on-chip routing algorithms, which use the coordinates of three adjacent zeros in the ...
Added: July 8, 2026
Algorithmic overlaps as thermodynamic variables: From local to cluster Monte Carlo dynamics in critical phenomena
Pilé I., Shchur L., Deng Y., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 Article 014101
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Swendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for models in different universality classes: Ising model, Potts model with three components, and four-state Potts model. The overlap of two ...
Added: July 6, 2026
Proceedings of the 9th International School-Seminar on Nonlinear Analysis and Extremal Problems (NLA-2026). Irkutsk, Russia, June 22–26, 2026. Irkutsk : ISDCT SB RAS, 2026, 326 p.
Irkutsk: ISDCT SB RAS, 2026.
We study a model problem on the filtration of a conducting fluid through a porous layer. A porous medium is presented as an assemblage of identical spherical cells. Each cell consists of a porous core and liquid shell. We derive apriori estimates for flow characteristics which show the specific behavior of the fluid. Our estimates are validated numerically. ...
Added: July 5, 2026
Журнал Телекоммуникации №1 за 2026
М.: Наука и технологии, 2026.
«Телекоммуникации» ежемесячный рецензируемый производственный, информационно-аналитический и учебно-методический журнал выходит в свет с июля 2000 г. Для руководителей и работников промышленности, научно-исследовательских и проектно-конструкторских институтов, высших учебных заведений, аспирантов и студентов, а также для специалистов, разрабатывающих, выпускающих и эксплуатирующих средства телекоммуникаций. Новости разработок и производства, прогнозы развития, защита информации, Нормативные, справочные, аналитические и учебно-методические материалы. Переход к глобальному информационному ...
Added: July 4, 2026
"Труды МФТИ" Том 17, № 4 (68) (2025)
МФТИ, 2025.
абота  редакции  научного журнала «Труды Московского физико-технического института» (кратко «Труды МФТИ»), редакционной коллегии и редакционного совета осуществляется в соответствии с Положением, утвержденным ректором института. В состав редакционной коллегии входят руководители института, факультетов, институтских и факультетских кафедр. Главный редактор журнала —президент МФТИ, член-корр. РАН Кудрявцев Н.Н.   Журнал «Труды МФТИ» входит в базу данных РИНЦ (Российский Индекс Научного Цитирования) и доступен в электронной ...
Added: July 4, 2026
Graph Games and Logic Design. Recent Developments and Further Directions. (TREN, volume 66)
Springer, 2026.
This book presents established and new research on the close connections between graph games and systems of logic, particularly existing and newly designed modal logics. The volume utilizes two graph games – the sabotage game and the hide-and-seek game – to demonstrate the natural interplay between designing new graph games and exploring new kinds of ...
Added: June 30, 2026
On Ω-stable 3-diffeomorphism with a solid or thickened surfaced basic set
Pochinka O., Barinova M., Journal of Geometry and Physics 2026 Vol. 228 P. 1–8
In the present paper we consider an Ω-stable 3-diffeomorphism with a solid or thickened surfaced non-trivial basic set. Such basic sets include, for instance, all one-dimensional expanding attractors and those two-dimensional basic sets that are not expanding. We prove that the chain recurrent set of every such a diffeomorphism necessarily contains at least two non-trivial ...
Added: June 30, 2026
Почти пустые симплексы и полиэдры Клейна
German O., Illarionov A., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 3–18
Пусть симплекс с целочисленными вершинами - содержащий ровно одну целочисленную точку, отличную от своих вершин. В работе доказывается, что если точка находится во внутренности симплекса или в относительной внутренности некоторой гиперграни симплекса, то объем симплекса ограничен величиной, зависящей только от размерности, в противном случае объем симплекса может быть сколь угодно большим. Этот результат применяется для вывода асимптотической формулы для среднего числа вершин полиэдров ...
Added: June 29, 2026
On the problem of optimal fair exchange
Kolesnikov A., Popova S., / Series arXiv "math". 2024.
We consider the problem of optimal exchange which can be formulated as a kind of optimal transportation problem. The existence of an optimal solution and a duality theorem for the optimal exchange problem are proved in case of completely regular topological spaces. We show the connection between the problem of optimal exchange and the optimal ...
Added: December 20, 2024
Обзор выпуклой оптимизации марковских процессов принятия решений
Rudenko V., Yudin N., Васин А. А., Компьютерные исследования и моделирование 2023 Т. 15 № 2 С. 329–353
This article reviews both historical achievements and modern results in the field of Markov Decision Process (MDP) and convex optimization. This review is the first attempt to cover the field of reinforcement learning in Russian in the context of convex optimization. The fundamental Bellman equation and the criteria of optimality of policy — strategies based on it, ...
Added: November 29, 2024
On a simple connection between Δ-modular ILP and LP, and a new bound on the number of integer vertices
Gribanov D., Malyshev D., Shumilov I., Operations Research Forum 2024 Vol. 5 Article 32
In our note, we present a very simple and short proof of a new interesting fact about the faces of an integer hull of a given rational polyhedron. This fact has a complete analog in linear programming theory and can be useful to establish new constructive upper bounds on the number of vertices in an integer hull of ...
Added: April 4, 2024
Exact Algorithm for Generating H-Cores in Simplified Lattice-Based Protein Model
Ignatov A., , in: 14th International Conference, OPTIMA 2023, Petrovac, Montenegro, September 18–22, 2023, Revised Selected Papers. Communications in Computer and Information Science (CCIS, volume 1913)Vol. 1913.: Springer, 2023. P. 173–187.
Modeling protein folding, which is the process by which a protein obtains its spacial shape, still remains a challenging problem. Protein geometry might be simplified by using the coarse-grained models. The highest level of simplification is achieved in HP-models where only polarity of amino acid residues is considered, and the unified monomers are located in nodes ...
Added: January 18, 2024
Auctions and mass transportation
Kolesnikov A., / Series arXiv "math". 2023.
In this survey paper we present classical and recent results relating the auction design  and the optimal transportation theory. ...
Added: December 13, 2023
Wasserstein Asymptotics for Brownian Motion on the Flat Torus and Brownian Interlacements
Mariani M., Trevisan D., Stochastic Processes and their Applications 2025 Vol. 183
Added: November 27, 2023
О безопасности схемы биометрической аутентификации, основанной на нейронной сети
Маршалко Г. Б., Математические вопросы криптографии 2014 Vol. 5 No. 2 P. 87–98
We show that neuron weights used in neural network-based biometric authentication scheme defined in GOST R 52633 standard series contain all the information on biometric data and secret key of the legitimate user. So, the complexity of evaluating (with known tables of neuron weights) the legitimate user's secret key is equivalent to the complexity of evaluating ...
Added: October 7, 2022
Beckmann's approach to multi-item multi-bidder auctions
Kolesnikov A., Zimin A., Sandomirskiy F. et al., / Series Theoretical Economics "arxiv.org". 2022. No. 2203.06837.
We consider the problem of revenue-maximizing Bayesian auction design with several i.i.d. bidders and several items. We show that the auction-design problem can be reduced to the problem of continuous optimal transportation introduced by Beckmann. We establish the strong duality between the two problems and demonstrate the existence of solutions. We then develop a new ...
Added: April 10, 2022
Blaschke–Santaló inequality for many functions and geodesic barycenters of measures
Kolesnikov A., Werner E., Advances in Mathematics 2022 Vol. 396 Article 108110
Motivated by the geodesic barycenter problem from optimal transportation theory, we prove a natural generalization of the Blaschke–Santaló inequality and the affine isoperimetric inequalities for many sets and many functions. We derive from it an entropy bound for the total Kantorovich cost appearing in the barycenter problem. We also establish a “pointwise Prékopa–Leindler inequality” and show a monotonicity property of the multimarginal Blaschke–Santaó functional. ...
Added: December 4, 2021
The multistochastic Monge–Kantorovich problem
Gladkov N., Kolesnikov A., Zimin A., Journal of Mathematical Analysis and Applications 2022 Vol. 506 No. 2 Article 125666
The multistochastic Monge–Kantorovich problem on the product X=∏i=1nXi of n spaces is a generalization of the multimarginal Monge–Kantorovich problem. For a given integer number 1≤k<n we consider the minimization problem ∫cdπ→inf on the space of measures with fixed projections onto every Xi1×…×Xik for arbitrary set of k indices {i1,…,ik}⊂{1,…,n}. In this paper we study basic properties of the multistochastic problem, including well-posedness, existence of a dual solution, boundedness and continuity of a dual ...
Added: December 4, 2021
The multistochastic Monge-Kantorovich problem
Gladkov N., Kolesnikov A., Zimin A., / Series arXiv "math". 2020.
The multistsochastic Monge--Kantorovich problem on the product   $X = \prod_{i=1}^n X_i$ of $n$ spaces is a generalization of the multimarginal Monge--Kantorovich problem. For a given integer number $1 \le k<n$ we consider the minimization problem $\int c d \pi \to \inf$ of the space of measures with fixed projections onto every  $X_{i_1} \times \dots \times ...
Added: August 21, 2020
An Explicit Solution for a Multimarginal Mass Transportation Problem
Gladkov N., Zimin A., SIAM Journal on Mathematical Analysis 2020 Vol. 52 No. 4 P. 3666–3696
We construct an explicit solution for the multimarginal transportation problem on the unit cube $[0, 1]^3$ with the cost function $xyz$ and one-dimensional uniform projections. We show that the primal problem is concentrated on a set with a nonconstant local dimension and admits many solutions, whereas the solution to the corresponding dual problem is unique ...
Added: August 21, 2020
A Constrained Shortest Path Scheme for Virtual Network Service Management
Chemodanov D., Esposito F., Calyam P. et al., IEEE Transactions on Network and Service Management 2019 Vol. 16 No. 1 P. 127–142
Virtual network services that span multiple data centers are important to support emerging data-intensive applications in fields such as bioinformatics and retail analytics. Successful virtual network service composition and maintenance requires flexible and scalable “constrained shortest path management” both in the management plane for virtual network embedding (VNE) or network function virtualization service chaining (NFV-SC), ...
Added: December 3, 2019
Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measures.
Bogachev V., Roeckner M., Shaposhnikov S., Journal of Functional Analysis 2019 Vol. 276 No. 12 P. 3681–3713
Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measures has been studied. ...
Added: November 16, 2019
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit