Zobrazeno 1 - 10
of 132
pro vyhledávání: '"Vorotnikov, Dmitry A."'
Autor:
Telciyan, Ayk, Vorotnikov, Dmitry
We study the equations of overdamped motion of an inextensible triod with three fixed ends and a free junction under the action of gravity. The problem can be expressed as a system of PDE that involves unknown Lagrange multipliers and non-standard bo
Externí odkaz:
http://arxiv.org/abs/2201.05547
If $u : \Omega\subset \mathbb{R}^d \to {\rm X}$ is a harmonic map valued in a metric space ${\rm X}$ and ${\sf E} : {\rm X} \to \mathbb{R}$ is a convex function, in the sense that it generates an ${\rm EVI}_0$-gradient flow, we prove that the pullbac
Externí odkaz:
http://arxiv.org/abs/2107.09589
In this short note we review the dynamical Schr\"odinger problem on the non-commutative Fisher-Rao space of positive semi-definite matrix-valued measures. The presentation is meant to be self-contained, and we discuss in particular connections with G
Externí odkaz:
http://arxiv.org/abs/2104.00383
In this paper we introduce the dynamical Schr\"odinger problem on abstract metric spaces, defined for a wide class of entropy and Fisher information functionals. Under very mild assumptions we prove a generic Gamma-convergence result towards the geod
Externí odkaz:
http://arxiv.org/abs/2012.12005
We present a self-contained and comprehensive study of the Fisher-Rao space of matrix-valued non-commutative probability measures, and of the related Hellinger space. Our non-commutative Fisher-Rao space is a natural generalization of the classical c
Externí odkaz:
http://arxiv.org/abs/2007.09042
Publikováno v:
In Advances in Mathematics 1 August 2023 426
Autor:
Vorotnikov, Dmitry
We study a rather general class of optimal "ballistic" transport problems for matrix-valued measures. These problems naturally arise, in the spirit of \emph{Y. Brenier. Comm. Math. Phys. (2018) 364(2) 579-605}, from a certain dual formulation of nonl
Externí odkaz:
http://arxiv.org/abs/1905.06059
We study the behaviour of various Lyapunov functionals (relative entropies) along the solutions of a family of nonlinear drift-diffusion-reaction equations coming from statistical mechanics and population dynamics. These equations can be viewed as gr
Externí odkaz:
http://arxiv.org/abs/1904.04112
We study nonlinear degenerate parabolic equations of Fokker-Planck type which can be viewed as gradient flows with respect to the recently introduced spherical Hellinger-Kantorovich distance. The driving entropy is not assumed to be geodesically conv
Externí odkaz:
http://arxiv.org/abs/1809.03430
Autor:
Brenier, Yann, Vorotnikov, Dmitry
We suggest a new way of defining optimal transport of positive-semidefinite matrix-valued measures. It is inspired by a recent rendering of the incompressible Euler equations and related conservative systems as concave maximization problems. The main
Externí odkaz:
http://arxiv.org/abs/1808.05064