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A Game-Theoretic Perspective on Coalition Formation

Debraj Ray

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199207954
eISBN:
9780191709104
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199207954.001.0001
Subject:
Economics and Finance, Financial Economics

The formation of coalitions to achieve both collaborative and competitive goals is a phenomenon we see all around us. The list of examples of this phenomenon is long and varied: production cartels, ... More


Coalitions, Cooperation and Noncooperation

Debraj Ray

in A Game-Theoretic Perspective on Coalition Formation

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199207954
eISBN:
9780191709104
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199207954.003.0003
Subject:
Economics and Finance, Financial Economics

This chapter describes in greater detail what the phrases ‘cooperation within coalitions’ and ‘non-cooperation across coalitions’ mean in this book. It develops the idea of coalitional equilibrium, ... More


Relativistic gases

Stephen J. Blundell and Katherine M. Blundell

in Concepts in Thermal Physics

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199562091
eISBN:
9780191718236
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199562091.003.0025
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter repeats the derivation of the partition function for a gas, and hence of the other thermodynamic properties that can be obtained from it, but this time includes relativistic effects. It ... More


Statement B and the Yang-Baxter Equation

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0019
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter reinterprets Statements A and B in a different context, and yet again directly proves that the reinterpreted Statement B implies the reinterpreted Statement A in Theorem 19.10. The ... More


The partition function

Stephen J. Blundell and Katherine M. Blundell

in Concepts in Thermal Physics

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199562091
eISBN:
9780191718236
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199562091.003.0020
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter introduces the partition function, which encodes all the information concerning the states of a system and their thermal occupation. Topics discussed include writing down the partition ... More


Advanced Statistical Mechanics

Barry M McCoy

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199556632
eISBN:
9780191723278
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556632.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book begins where elementary books and courses leave off and covers the advances made in statistical mechanics in the past fifty years. The book is divided into three parts. The first part is on ... More


CHERN–SIMONS THEORY AND KNOT INVARIANTS

Marcos Mariño

in Chern-Simons Theory, Matrix Models, and Topological Strings

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568490
eISBN:
9780191717604
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568490.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter presents various aspects of Chern-Simons theory. In a groundbreaking paper, Witten (1989) showed that Chern-Simons gauge theory, which is a quantum field theory in three dimensions, ... More


The Ising model in two dimensions: summary of results

Barry M. McCoy

in Advanced Statistical Mechanics

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199556632
eISBN:
9780191723278
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556632.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter summarizes the many results of the exactly solved Ising model in two dimensions at H = 0 including: the partition function, free energy, spontaneous magnetization, the Toeplitz ... More


Statistical mechanics of an ideal gas

Stephen J. Blundell and Katherine M. Blundell

in Concepts in Thermal Physics

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199562091
eISBN:
9780191718236
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199562091.003.0021
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

The partition function is a sum over all the states of a system of the relevant Boltzmann factors. Constructing the partition function is the first step to deriving all the thermodynamic properties ... More


FLOWS AND FERROMAGNETS

Geoffrey Grimmett

in Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198571278
eISBN:
9780191718885
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198571278.003.0008
Subject:
Mathematics, Probability / Statistics

The Tutte polynomial and its relatives play important roles in matroid theory, computational complexity, and models of statistical physics. They provide the natural way to count and relate a variety ... More


Crystals and p-adic Integration

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0020
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter describes the properties of Kashiwara's crystal and its role in unipotent p-adic integrations related to Whittaker functions. In many cases, integrations of representation theoretic ... More


PATH INTEGRALS IN QUANTUM MECHANICS

Jean Zinn-Justin

in Path Integrals in Quantum Mechanics

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198566748
eISBN:
9780191717994
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566748.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter constructs the path integral associated with the statistical operator e -βH in the case of Hamiltonians of the simple form p2/2m + V (q). The path ... More


Bimolecular reactions, transition-state theory

Niels E. Henriksen and Flemming Y. Hansen

in Theories of Molecular Reaction Dynamics: The Microscopic Foundation of Chemical Kinetics

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199203864
eISBN:
9780191708251
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199203864.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses an approximate approach — transition-state theory — to the calculation of rate constants for bimolecular reactions. A reaction coordinate is identified from a normal-mode ... More


Irreversible Agreements: Symmetric Games

Debraj Ray

in A Game-Theoretic Perspective on Coalition Formation

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199207954
eISBN:
9780191709104
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199207954.003.0005
Subject:
Economics and Finance, Financial Economics

This chapter studies a special case of the framework introduced in Chapter 4, one that relies on ‘symmetry’. It focuses on symmetric partition functions: such functions have the property that the ... More


CLASSICAL AND QUANTUM STATISTICAL PHYSICS

Jean Zinn-Justin

in Path Integrals in Quantum Mechanics

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198566748
eISBN:
9780191717994
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566748.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter provides a simple physical interpretation to the formal continuum limit that has led, from an integral over position variables corresponding to discrete times, to a path integral. It ... More


PATH INTEGRALS AND HOLOMORPHIC FORMALISM

Jean Zinn-Justin

in Path Integrals in Quantum Mechanics

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198566748
eISBN:
9780191717994
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566748.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter introduces the holomorphic representation of quantum mechanics, because it allows a study of the properties of boson systems both from the point of view of evolution and of quantum ... More


PARTITION FUNCTION AND SPECTRUM

Jean Zinn-Justin

in Path Integrals in Quantum Mechanics

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198566748
eISBN:
9780191717994
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566748.003.0003
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

A direct application of the calculation of the partition function is provided by determining the spectrum of a Hamiltonian (which is assumed to be discrete, for simplicity). In this chapter, only ... More


PATH INTEGRALS: FERMIONS

Jean Zinn-Justin

in Path Integrals in Quantum Mechanics

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198566748
eISBN:
9780191717994
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566748.003.0007
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

The methods that have been described in previous chapters can be used to study general quantum Bose systems. They are based in a direct way on the introduction of a generating function of symmetric ... More


Density operators and Wigner functions

Helmut Hofmann

in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198504016
eISBN:
9780191708480
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504016.003.0019
Subject:
Physics, Nuclear and Plasma Physics

This chapter introduces density operators and matrices for many-body systems, and explains their reduction to one- and two-body densities. Starting from the Slater determinant, the latter are ... More


The chemical potential

Stephen J. Blundell and Katherine M. Blundell

in Concepts in Thermal Physics

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199562091
eISBN:
9780191718236
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199562091.003.0022
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter extends the results on partition functions to systems in which the number of particles can vary. This allows the definition of the chemical potential and introduces the grand partition ... More


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