Mathematical Statistical Physics
Lecture Notes of the Les Houches Summer School 2005
- 1st Edition, Volume 83 - August 24, 2006
- Imprint: Elsevier Science
- Editors: Anton Bovier, François Dunlop, Aernout Van Enter, Frank Den Hollander, Jean Dalibard
- Language: English
- Hardback ISBN:9 7 8 - 0 - 4 4 4 - 5 2 8 1 3 - 1
- eBook ISBN:9 7 8 - 0 - 0 8 - 0 4 7 9 2 3 - 1
The proceedings of the 2005 les Houches summer school on Mathematical Statistical Physics give and broad and clear overview on this fast developing area of interest to both… Read more
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The proceedings of the 2005 les Houches summer school on Mathematical Statistical Physics give and broad and clear overview on this fast developing area of interest to both physicists and mathematicians.
- Introduction to a field of math with many interdisciplinary connections in physics, biology, and computer science
- Roadmap to the next decade of mathematical statistical mechanics
- Volume for reference years to come
Libraries of mathematics and physics, Individual scientists
Lecturers who Contributed to this volume
ÉCOLE D’ÉTÉ DE PHYSIQUE DES HOUCHES
École de Physique des Houches
Previous sessions
Organizers
Lecturers
Participants
Preface
Informal Seminars
Random Matrices and Determinantal Processes
1 Introduction
2 Point processes
3 Non-intersecting paths and the Aztec diamond
4 Asymptotics
5 The corner growth model
Acknowledgement
Some Recent Aspects of Random Conformally Invariant Systems
Overview
Conformal Random Geometry
1 Preamble
2 Introduction
3 Intersections of random walks
4 Mixing random & self-avoiding walks
5 Percolation clusters
Random Motions in Random Media
1 Introduction
2 RWRE
3 RCM
4 Back to RWRE
Effective criterion:
5 Diffusions in random environment
An Introduction to Mean Field Spin Glas Theory: Methods and Results
1 Introduction
2 The mean field ferromagnetic model. Convexity and cavity methods
3 The mean field spin glass model. Basic definitions
4 The interpolation method and its generalizations
5 The thermodynamic limit and the variational bounds
6 The Parisi representation for the free energy
7 Conclusion and outlook for future developments
Acknowledgments
Short-Range Spin Glasses: Selected Open Problems
1 Introduction
2 The Fortuin-Kasteleyn random cluster representation and phase transitions
3 Spin glass ground states and invasion percolation
4 Ground state multiplicity in the 2D EA spin glass
Acknowledgment
Computing the Number of Metastable States in Infinite-Range Models
Acknowledgments
Dynamics of Trap Models
1 Introduction
2 Definition of the Bouchaud trap model
2.2. Assumption 2.2.
2.3. Assumption 2.3.
2.1 Examples of trap models
2.2 Natural questions on trap models
2.3 References
3 The one-dimensional trap model
3.3 Aging results
3.4 Subaging results
3.5 Behaviour of the aging functions on different time scales
4 The trap model in dimension larger than one
4.3 Aging results
4.4 The coarse-graining procedure
4.5 References
5 The arcsine law as a universal aging scheme
6 Applications of the arcsine law
Appendix A Subordinators
Quantum Entropy and Quantum Information
1 Introduction
2 Rudiments of Classical Information Theory
3 Introduction to Quantum Information Theory
4 Open systems
5 Quantum entropy
6 Data compression in Quantum Information Theory
7 Quantum channels and additivity
Acknowledgments
Two Lectures on Iterative Coding and Statistical Mechanics
1 Introduction
2 Codes on graphs
3 A simple-minded bound and belief propagation
4 Density evolution a.k.a. distributional recursive equations
5 The area theorem and some general questions
6 Historical and bibliographical note
Evolution in Fluctuating Populations
1 Introduction
Acknowledgement
2 Some classical coalescent theory
4 Spatial structure and the Malécot formula
5 Spatial models
Multi-Scale Analysis of Population Models
1 Spatial diffusion models of population genetics
2 Duality and representation via coalescent processes
Elements of Nonequilibrium Statistical Mechanics
1 Elements of introduction
2 Elements of an H-theorem
3 Elements of heat conduction
4 Lagrangian approach
5 A little entropology
6 Closed systems
7 Open systems
8 Why is it useful?
9 What is missing — among other things?
Mathematical Aspects of the Abelian Sandpile Model
Open question
Gibbsianness and Non-Gibbsianness in Lattice Random Fields
1 Historical remarks and purpose of the course
2 Setup, notation, and basic notions
3 Probability kernels, conditional probabilities, and statistical mechanics
4 What it takes to be Gibbsian
5 What it takes to be non-Gibbsian
Acknowledgments
Simulation of Statistical Mechanics Models
1 Overview
2 The Swendsen–Wang algorithm: some recent progress
Acknowledgments
- Edition: 1
- Volume: 83
- Published: August 24, 2006
- Imprint: Elsevier Science
- Language: English
JD
Jean Dalibard
Jean Dalibard works in the field of atomic physics and quantum optics. His recent activities is centered on the physics of cold quantum gases, in particular Bose-Einstein condensation.
Affiliations and expertise
Laboratoire Kastler Brossel, ENS, Paris, FranceRead Mathematical Statistical Physics on ScienceDirect