Author | Kipnis, Claude. author |
---|---|
Title | Scaling Limits of Interacting Particle Systems [electronic resource] / by Claude Kipnis, Claudio Landim |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999 |
Connect to | http://dx.doi.org/10.1007/978-3-662-03752-2 |
Descript | XVI, 444 p. online resource |
1. An Introductory Example: Independent Random Walks -- 2. Some Interacting Particle Systems -- 3. Weak Formulations of Local Equilibrium -- 4. Hydrodynamic Equation of Symmetric Simple Exclusion Processes -- 5. An Example of Reversible Gradient System: Symmetric Zero Range Processes -- 6. The Relative Entropy Method -- 7. Hydrodynamic Limit of Reversible Nongradient Systems -- 8. Hydrodynamic Limit of Asymmetric Attractive Processes -- 9. Conservation of Local Equilibrium for Attractive Systems -- 10. Large Deviations from the Hydrodynamic Limit -- 11. Equilibrium Fluctuations of Reversible Dynamics -- Appendices -- 1. Markov Chains on a Countable Space -- 1.1 Discrete Time Markov Chains -- 1.2 Continuous Time Markov Chains -- 1.3 Kolmogorovโs Equations, Generators -- 1.4 Invariant Measures, Reversibility and Adjoint Processes -- 1.5 Some Martingales in the Context of Markov Processes -- 1.6 Estimates on the Variance of Additive Functionals of Markov Processes -- 1.7 The Feynman-Kac Formula -- 1.8 Relative Entropy -- 1.9 Entropy and Markov Processes -- 1.10 Dirichlet Form -- 1.11 A Maximal Inequality for Reversible Markov Processes -- 2. The Equivalence of Ensembles, Large Deviation Tools and Weak Solutions of Quasi-Linear Differential Equations -- 2.1 Local Central Limit Theorem and Equivalence of Ensembles -- 2.2 On the Local Central Limit Theorem -- 2.3 Remarks on Large Deviations -- 2.4 Weak Solutions of Nonlinear Parabolic Equations -- 2.5 Entropy Solutions of Quasi-Linear Hyperbolic Equations -- 3. Nongradient Tools: Spectral Gap and Closed Forms -- 3.1 On the Spectrum of Reversible Markov Processes -- 3.2 Spectral Gap for Generalized Exclusion Processes -- 3.4 Closed and Exact Forms -- 3.5 Comments and References -- References