最優輸運（第1分冊） [Optimal Transport Old and New Part 1] pdf epub mobi txt 電子書下載 2025

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[法] 維拉尼著

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齣版社：世界圖書齣版公司

ISBN：9787510077906

版次：1

商品編碼：11582551

包裝：平裝

外文名稱：Optimal Transport Old and New Part 1

開本：24開

齣版時間：2014-07-01

用紙：膠版紙

頁數：729

正文語種：英文

具體描述

內容簡介

　　When I was first approached for the 2005 edition of the Saint-Flour Probability Summer School, I was intrigued, flattered and scared. l Apart from the challenge posed by the teaching of a rather analytical
　　subject to a probabilistic audience, there was the danger of producing a remake of my recent book Topics in, Optimal Transportation.

內頁插圖

Preface
Conventions
Introduction
1 Couplings and changes of variables
2 Three examples of coupling techniques
3 The founding fathers of optimal transport

Part Ⅰ Qualitative description of optimal transport
4 Basic properties
5 Cyclical monotonicity and Kantorovich duality
6 The Wasserstein distances
7 Displacement interpolation
8 The Monge-Mather shortening principle
9 Solution of the Monge problem I: Global approach
10 Solution of the Monge problem II: Local approach
11 The Jacobian equation
12 Smoothness
13 Qualitative picture

Part Ⅱ Optimal transport and Riemannian geometry
14 Ricci curvature
15 Otto calculus
16 Displacement convexity I
17 Displacement convexity II
18 Volume control
19 Density control and local regularity
20 Infinitesimal displacement convexity
21 Isoperimetric-type inequalities
22 Concentration inequalities
23 Gradient flows I
24 Gradient flows II: Qualitative properties
25 Gradient flows III: Functional inequalities

Part Ⅲ Synthetic treatment of Ricci curvature
26 Analytic and synthetic points of view
27 Convergence of metric-measure spaces
28 Stability of optimal transport
……
Conclusions and open problems

前言/序言

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