On Sudakov S Type Decomposition Of Transference Plans With Norm Costs
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On Sudakov S Type Decomposition Of Transference Plans With Norm Costs
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Author : Stefano Bianchini
language : en
Publisher:
Release Date : 2018
On Sudakov S Type Decomposition Of Transference Plans With Norm Costs written by Stefano Bianchini and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Decomposition (Mathematics) categories.
On Sudakov S Type Decomposition Of Transference Plans With Norm Costs
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Author : Stefano Bianchini
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-02-23
On Sudakov S Type Decomposition Of Transference Plans With Norm Costs written by Stefano Bianchini and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-23 with Decomposition (Mathematics) categories.
The authors consider the original strategy proposed by Sudakov for solving the Monge transportation problem with norm cost with , probability measures in and absolutely continuous w.r.t. . The key idea in this approach is to decompose (via disintegration of measures) the Kantorovich optimal transportation problem into a family of transportation problems in , where are disjoint regions such that the construction of an optimal map is simpler than in the original problem, and then to obtain by piecing together the maps . When the norm is strictly convex, the sets are a family of -dimensional segments determined by the Kantorovich potential called optimal rays, while the existence of the map is straightforward provided one can show that the disintegration of (and thus of ) on such segments is absolutely continuous w.r.t. the -dimensional Hausdorff measure. When the norm is not strictly convex, the main problems in this kind of approach are two: first, to identify a suitable family of regions on which the transport problem decomposes into simpler ones, and then to prove the existence of optimal maps. In this paper the authors show how these difficulties can be overcome, and that the original idea of Sudakov can be successfully implemented. The results yield a complete characterization of the Kantorovich optimal transportation problem, whose straightforward corollary is the solution of the Monge problem in each set and then in . The strategy is sufficiently powerful to be applied to other optimal transportation problems.
High Dimensional Probability
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Author : Roman Vershynin
language : en
Publisher: Cambridge University Press
Release Date : 2018-09-27
High Dimensional Probability written by Roman Vershynin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-27 with Business & Economics categories.
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Optimal Transport For Applied Mathematicians
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Author : Filippo Santambrogio
language : en
Publisher: Birkhäuser
Release Date : 2015-10-17
Optimal Transport For Applied Mathematicians written by Filippo Santambrogio and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-17 with Mathematics categories.
This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource.
Optimal Transportation And Action Minimizing Measures
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Author : Alessio Figalli
language : en
Publisher: Edizioni della Normale
Release Date : 2008-07-17
Optimal Transportation And Action Minimizing Measures written by Alessio Figalli and has been published by Edizioni della Normale this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-17 with Mathematics categories.
In this book we describe recent developments in the theory of optimal transportation, and some of its applications to fluid dynamics. Moreover we explore new variants of the original problem, and we try to figure out some common (and sometimes unexpected) features in this emerging variety of problems . In Chapter 1 we study the optimal transportation problem on manifolds with geometric costs coming from Tonelli Lagrangians, while in Chapter 2 we consider a generalization of the classical transportation problem called the optimal irrigation problem. Then, Chapter 3 is about the Brenier variational theory of incompressible flows, which concerns a weak formulation of the Euler equations viewed as a geodesic equation in the space of measure-preserving diffeomorphism. Chapter 4 is devoted to the study of regularity and uniqueness of solutions of Hamilton-Jacobi equations applying the Aubry-Mather theory. Finally, the last chapter deals with a DiPerna-Lions theory for martingale solutions of stochastic differential equations.
Differential Equations Methods For The Monge Kantorovich Mass Transfer Problem
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Author : Lawrence C. Evans
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Differential Equations Methods For The Monge Kantorovich Mass Transfer Problem written by Lawrence C. Evans and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
In this volume, the authors demonstrate under some assumptions on $f $, $f $ that a solution to the classical Monge-Kantorovich problem of optimally rearranging the measure $\mu{ }=f dx$ onto $\mu =f dy$ can be constructed by studying the $p$-Laplacian equation $- \roman{div}(\vert DU_p\vert p-2}Du_p)=f -f $ in the limit as $p\rightarrow\infty$. The idea is to show $u_p\rightarrow u$, where $u$ satisfies $\vert Du\vert\leq 1, -\roman{div}(aDu)=f -f $ for some density $a\geq0$, and then to build a flow by solving a nonautonomous ODE involving $a, Du, f $ and $f $
Holomorphic Automorphic Forms And Cohomology
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Author : Roelof Bruggeman
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29
Holomorphic Automorphic Forms And Cohomology written by Roelof Bruggeman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Algebraic topology categories.
Neckpinch Dynamics For Asymmetric Surfaces Evolving By Mean Curvature Flow
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Author : Zhou Gang
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-05-29
Neckpinch Dynamics For Asymmetric Surfaces Evolving By Mean Curvature Flow written by Zhou Gang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-29 with Asymptotic expansions categories.
Poincare S Legacies Part I
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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Poincare S Legacies Part I written by Terence Tao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Focuses on ergodic theory, combinatorics, and number theory. This book discusses a variety of topics, ranging from developments in additive prime number theory to expository articles on individual mathematical topics such as the law of large numbers and the Lucas-Lehmer test for Mersenne primes.
From Vertex Operator Algebras To Conformal Nets And Back
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Author : Sebastiano Carpi
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-09
From Vertex Operator Algebras To Conformal Nets And Back written by Sebastiano Carpi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-09 with Conformal invariants categories.
The authors consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. They present a general procedure which associates to every strongly local vertex operator algebra V a conformal net AV acting on the Hilbert space completion of V and prove that the isomorphism class of AV does not depend on the choice of the scalar product on V. They show that the class of strongly local vertex operator algebras is closed under taking tensor products and unitary subalgebras and that, for every strongly local vertex operator algebra V, the map W↦AW gives a one-to-one correspondence between the unitary subalgebras W of V and the covariant subnets of AV.