TY - BOOK ID - 2697088 TI - Scaling limits of interacting particle systems AU - Kipnis, Claude AU - Landim, Claudio PY - 1999 VL - 320 SN - 3540649131 3642084443 3662037521 9783540649137 PB - Berlin ; Heidelberg ; New York Springer Verlag DB - UniCat KW - Fysica [Mathematische ] KW - Fysica [Wiskundige ] KW - Lois d'échelle (Physique statistique) KW - Markoff processes KW - Markov [Processus de ] KW - Markov models KW - Markov processen KW - Markov processes KW - Markov-processen KW - Mathematical physics KW - Mathematische fysica KW - Physical mathematics KW - Physics -- Mathematics KW - Physics [Mathematical ] KW - Physique -- Mathématiques KW - Physique -- Méthodes mathématiques KW - Physique mathématique KW - Physique théorique KW - Probabiliteit--Theorie KW - Probabiliteitstheorie KW - Probabilities KW - Probabilité [Théorie de la ] KW - Probabilités KW - Processus de Markov KW - Scaling laws (Statistical physics) KW - Schaalwetten (Statistische fysica) KW - Waarschijnlijkheid--Theorie KW - Waarschijnlijkheidstheorie KW - Wiskundige fysica KW - Hydrodynamics KW - Mathematics KW - Probabilities. KW - Mathematical physics. KW - Probability Theory and Stochastic Processes. KW - Theoretical, Mathematical and Computational Physics. KW - Physics KW - Probability KW - Statistical inference KW - Combinations KW - Chance KW - Least squares KW - Mathematical statistics KW - Risk KW - Hydrodynamics - Mathematics UR - https://www.unicat.be/uniCat?func=search&query=sysid:2697088 AB - 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. ER -