Basic examples

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Basic examples / Michel Talagrand

資料種別:: 図書
出版情報:: Berlin : Springer, c2011
形態:: xviii, 485 p. ; 25 cm
シリーズ名:: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge . A series of modern surveys in mathematics ; v. 54 . Mean field models for spin glasses / Michel Talagrand ; v. 1 <BA00035552>
著者名:: Talagrand, Michel, 1952- <DA05475876>
ISBN:: 9783642152016 [3642152015]
書誌ID:: BB04199129

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注記:

Includes bibliographical references (p. 465-473) and index

主題:

数学

言語:

英語

目次情報:

Introduction

The Sherrington-Kirkpatrick Model / 1：

Notations and Simple Facts / 1.1：

Gaussian Interpolation and the Smart Path Method / 1.3：

Latala's Argument / 1.4：

A Kind of Central Limit Theorem / 1.5：

The Cavity Method / 1.6：

Gibbs' Measure; the TAP Equations / 1.7：

Second Moment Computations and the Almeida-Thouless Line / 1.8：

Beyond the AT Line / 1.9：

Central Limit Theorem for the Overlaps / 1.10：

Non Gaussian Behavior: Hanen's Theorem / 1.11：

The SK Model with d-component Spins / 1.12：

The Physicist's Replica Method / 1.13：

Notes and Comments / 1.14：

The Perceptron Model / 2：

The Smart Path / 2.1：

Cavity in M / 2.3：

The Replica Symmetric Solution / 2.4：

Exponential Inequalities / 2.5：

The Shcherbina and Tirozzi Model / 2.6：

The Power of Convexity / 3.1：

The Replica-Symmetric Equations / 3.2：

Controlling the Solutions of the RS Equations / 3.3：

The Hopfield Model / 3.4：

Introduction: The Curie-Weiss Model / 4.1：

Local Convexity and the Hubbard-Stratonovitch Transform / 4.2：

The Bovier-Gayrard Localization Theorem / 4.3：

Selecting a State with an External Field / 4.4：

Controlling the Overlaps / 4.5：

Approximate Integration by Parts and the Replica-Symmetric Equations / 4.6：

The V-statistics Model / 4.7：

The New Equation / 5.1：

The Replica-Symmetric Solution / 5.5：

The Diluted SK Model and the K-Sat Problem / 6：

Pure State / 6.1：

The Functional Order Parameter / 6.3：

The Franz-Leone Bound / 6.4：

Continuous Spins / 6.6：

An Assignment Problem / 6.7：

Overview of the Proof / 7.1：

Decoupling / 7.3：

Empirical Measures / 7.5：

Operators / 7.6：

Elements of Probability Theory / 7.7：

How to Use this Appendix / A.1：

Differentiation Inside an Expectation / A.2：

Gaussian Random Variables / A.3：

Gaussian Integration by Parts / A.4：

Tail Estimates / A.5：

How to Use Tail Estimates / A.6：

Bernstein's Inequality / A.7：

?-Nets / A.8：

Random Matrices / A.9：

Poisson Random Variables and Point Processes / A.10：

Distances Between Probability Measures / A.11：

The Paley-Zygmund Inequality / A.12：

Differential Inequalities / A.13：

The Latala-Guerra Lemma / A.14：

Proof of Theorem 3.1.4 / A.15：

References

Index

Glossary

Introduction

The Sherrington-Kirkpatrick Model / 1：

Notations and Simple Facts / 1.1：

Gaussian Interpolation and the Smart Path Method / 1.3：

Latala's Argument / 1.4：

A Kind of Central Limit Theorem / 1.5：

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