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Wasserstein Asymptotics for Brownian Motion on the Flat Torus and Brownian Interlacements
Stochastic Processes and their Applications. 2025. Vol. 183.
Мариани М., Trevisan D.
Ключевые слова: Optimal transportation
Добавлено: 21 августа 2020 г.
Гладков Н. А., Зимин А. П., SIAM Journal on Mathematical Analysis 2020 Vol. 52 No. 4 P. 3666–3696
Добавлено: 21 августа 2020 г.
Mass transportation functionals on the sphere with applications to the logarithmic Minkowski problem
Колесников А. В., Moscow Mathematical Journal 2020 Vol. 20 No. 1 P. 67–91
Добавлено: 9 октября 2019 г.
Гладков Н. А., Колесников А. В., Зимин А. П., Calculus of Variations and Partial Differential Equations 2019 Vol. 58 No. 173 P. 1–33
Добавлено: 9 октября 2019 г.
Mass transportation functionals on the sphere with applications to the logarithmic Minkowski problem
Колесников А. В., / Series arXiv "math". 2018.
Добавлено: 31 июля 2018 г.
Колесников А. В., Лысенко Н. Ю., Theory of Stochastic Processes 2016 Vol. 21(37) No. 2 P. 22–28
We study the Monge--Kantorovich problem with one-dimensional marginals $\mu$ and $\nu$ and
the cost function $c = \min\{l_1, \ldots, l_n\}$
that equals the minimum of a finite number $n$ of affine functions $l_i$
satisfying certain non-degeneracy assumptions. We prove that the problem
is equivalent to a finite-dimensional extremal problem. More precisely, it is shown that the solution is concentrated
on ...
Добавлено: 30 декабря 2017 г.
Заев Д. А., Колесников А. В., Kyoto Journal of Mathematics 2017 Vol. 57 No. 2 P. 293–324
Добавлено: 30 декабря 2017 г.
Косоруков О. А., Journal of Computer and Systems Sciences International 2016 Vol. 55 No. 6 P. 1010–1015
Добавлено: 17 августа 2017 г.
Klartag B., Колесников А. В., Analysis Mathematica 2017 Vol. 43 No. 1 P. 67–88
According to a classical result of E. Calabi any hyperbolic affine hypersphere endowed with its natural Hessian metric has a non-positive Ricci tensor. The affine hyperspheres can be described as the level sets of solutions to the “hyperbolic” toric Kähler–Einstein equation eΦ = detD2Φ on proper convex cones. We prove a generalization of this theorem by showing ...
Добавлено: 17 апреля 2017 г.
Колесников А. В., Заев Д. А., Theory of Stochastic Processes 2015 Vol. 20(36) No. 2 P. 54–62
We study the Monge and Kantorovich transportation problems on R∞R∞ within the class of exchangeable measures. With the help of the de Finetti decomposition theorem the problem is reduced to an unconstrained optimal transportation problem on a Hilbert space. We find sufficient conditions for convergence of finite-dimensional approximations to the Monge solution. The result holds, in particular, ...
Добавлено: 8 июля 2016 г.
Колесников А., Bulletin des Sciences Mathematiques 2014 Vol. 138 No. 2 P. 165–198
Добавлено: 23 декабря 2015 г.
Колесников А. В., Milman E., Geometric Aspects of Functional Analysis, Israel Seminar 2014 Vol. 2116 P. 273–293
We generalize the classical Hardy and Faber-Krahn inequalities to arbitrary functions on a convex body Ω ⊂ R n , not necessarily vanishing on the boundary ∂Ω. This reduces the study of the Neumann Poincar´e constant on Ω to that of the cone and Lebesgue measures on ∂Ω; these may be bounded via the curvature ...
Добавлено: 13 апреля 2015 г.
Колесников А. В., Тихонов С., Calculus of Variations and Partial Differential Equations 2014 Vol. 49 No. 3-4 P. 1187–1197
Let \mu = e^{-V} \ dx be a probability measure and T = \nabla \Phi be the optimal transportation mapping pushing forward \mu onto a log-concave compactly supported measure \nu = e^{-W} \ dx. In this paper, we introduce a new approach to the regularity problem for the corresponding Monge--Amp{\`e}re equation e^{-V} = \det D^2 ...
Добавлено: 12 марта 2014 г.
Колесников А. В., Klartag B., / Series math "arxiv.org". 2013. No. 1402.2636.
Добавлено: 12 марта 2014 г.
Колесников А. В., Discrete and Continuous Dynamical Systems 2014 Vol. 34 No. 4 P. 1511–1532
Добавлено: 12 ноября 2013 г.
Kudryavtseva O., Nagapetyan T., Колесников А. В., Journal Mathematical Economics, Netherlands 2013 Vol. 49 P. 501–505
The famous Afriat’s theorem from the theory of revealed preferences establishes necessary and sufficient conditions for the existence of utility function for a given set of choices and prices. The result on the existence of a homogeneous utility function can be considered as a particular fact of the Monge–Kantorovich mass transportation theory. In this paper ...
Добавлено: 27 сентября 2013 г.
Колесников А. В., / Series math "arxiv.org". 2012. No. 1201.2342.
We study the optimal transportation mapping $\nabla \Phi : \mathbb{R}^d \mapsto \mathbb{R}^d$ pushing forward a probability measure $\mu = e^{-V} \ dx$ onto another probability measure $\nu = e^{-W} \ dx$. Following a classical approach of E. Calabi we introduce the Riemannian metric $g = D^2 \Phi$ on $\mathbb{R}^d$ and study spectral properties of the ...
Добавлено: 28 марта 2013 г.
Колесников А. В., / Series math "arxiv.org". 2009. No. 0904.1852.
Given two probability measures $\mu$ and $\nu$ we consider a mass transportation mapping $T$ satisfying 1) $T$ sends $\mu$ to $\nu$, 2) $T$ has the form $T = \phi \frac{\nabla \phi}{|\nabla \phi|}$, where $\phi$ is a function with convex sublevel sets.
We prove a change of variables formula for $T$. We also establish Sobolev estimates for ...
Добавлено: 27 марта 2013 г.
Колесников А. В., Bogachev V. I., Russian Mathematical Surveys 2012 Vol. 67 No. 5 P. 785–890
This article gives a survey of recent research related to the Monge-Kantorovich problem. Principle results are presented on the existence of solutions and their properties both in the Monge optimal transportation problem and the Kantorovich optimal plan problem, along with results on the connections between both problems and the cases when they are equivalent. Diverse ...
Добавлено: 12 февраля 2013 г.