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Statistical physics --- Scaling laws (Statistical physics) --- Renormalization (Physics) --- Lois d'échelle (Physique statistique) --- Renormalisation (Physique) --- Renormalization (Physics). --- Scaling laws (Statistical physics). --- Lois d'échelle (Physique statistique) --- Statistical physics. --- Physique statistique

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Physique --- Cinématique --- Kinematics --- Temps --- time --- Énergie --- energy --- Travail --- Labour --- Propriété magnétique --- Magnetic properties --- Électricité --- Electricity --- Champ électromagnétique --- Electromagnetic field --- Mécanique des fluides --- Fluid mechanics --- Température --- Temperature --- Vibration --- Audition --- Hearing --- Vision --- 53 --- Physics --- 53 Physics --- Bodybuilding. --- Temperature. --- Acqui 2006 --- Vecteur --- Thermodynamique --- Mouvement ondulatoire --- Optique --- Physique quantique --- Lois de newton --- Lois de kepler --- Lois de conservation --- Lois d'echelle

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The idea of writing up a book on the hydrodynamic behavior of interacting particle systems was born after a series of lectures Claude Kipnis gave at the University of Paris 7 in the spring of 1988. At this time Claude wrote some notes in French that covered Chapters 1 and 4, parts of Chapters 2, 5 and Appendix 1 of this book. His intention was to prepare a text that was as self-contained as possible. lt would include, for instance, all tools from Markov process theory ( cf. Appendix 1, Chaps. 2 and 4) necessary to enable mathematicians and mathematical physicists with some knowledge of probability, at the Ievel of Chung (1974), to understand the techniques of the theory of hydrodynamic Iimits of interacting particle systems. In the fall of 1991 Claude invited me to complete his notes with him and transform them into a book that would present to a large audience the latest developments of the theory in a simple and accessible form. To concentrate on the main ideas and to avoid unnecessary technical difficulties, we decided to consider systems evolving in finite lattice spaces and for which the equilibrium states are product measures. To illustrate the techniques we chose two well-known particle systems, the generalized exclusion processes and the zero-range processes. We also conceived the book in such a manner that most chapters can be read independently of the others. Here are some comments that might help readers find their way.

Fysica [Mathematische ] --- Fysica [Wiskundige ] --- Lois d'échelle (Physique statistique) --- Markoff processes --- Markov [Processus de ] --- Markov models --- Markov processen --- Markov processes --- Markov-processen --- Mathematical physics --- Mathematische fysica --- Physical mathematics --- Physics -- Mathematics --- Physics [Mathematical ] --- Physique -- Mathématiques --- Physique -- Méthodes mathématiques --- Physique mathématique --- Physique théorique --- Probabiliteit--Theorie --- Probabiliteitstheorie --- Probabilities --- Probabilité [Théorie de la ] --- Probabilités --- Processus de Markov --- Scaling laws (Statistical physics) --- Schaalwetten (Statistische fysica) --- Waarschijnlijkheid--Theorie --- Waarschijnlijkheidstheorie --- Wiskundige fysica --- Hydrodynamics --- Mathematics --- Probabilities. --- Mathematical physics. --- Probability Theory and Stochastic Processes. --- Theoretical, Mathematical and Computational Physics. --- Physics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Hydrodynamics - Mathematics

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The lace expansion is a powerful and flexible method for understanding the critical scaling of several models of interest in probability, statistical mechanics, and combinatorics, above their upper critical dimensions. These models include the self-avoiding walk, lattice trees and lattice animals, percolation, oriented percolation, and the contact process. This volume provides a unified and extensive overview of the lace expansion and its applications to these models. Results include proofs of existence of critical exponents and construction of scaling limits. Often, the scaling limit is described in terms of super-Brownian motion.

Percolation (Statistical physics) --- Scaling laws (Statistical physics) --- Mathematical statistics. --- Probabilities. --- Percolation (Physique statistique) --- Lois d'échelle (Physique statistique) --- Statistique mathématique --- Probabilités --- Electronic books. -- local. --- Percolation (Statistical physics). --- Scaling laws (Statistical physics). --- Mathematical statistics --- Probabilities --- Physics --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Mathematical Statistics --- Atomic Physics --- Probability --- Statistical inference --- Statistics, Mathematical --- Ratio and proportion (Statistical physics) --- Scale invariance (Statistical physics) --- Scaling hypothesis (Statistical physics) --- Scaling phenomena (Statistical physics) --- Statistical methods --- Mathematics. --- Combinatorics. --- Physics. --- Probability Theory and Stochastic Processes. --- Theoretical, Mathematical and Computational Physics. --- Combinations --- Chance --- Least squares --- Risk --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Combinatorics --- Algebra --- Mathematical analysis --- Math --- Science --- Physical laws --- Ranking and selection (Statistics) --- Statistical physics --- Statistics --- Sampling (Statistics) --- Lattice theory --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Mathematical physics. --- Physical mathematics