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- catalog abstract "Entropy inequalities, correlation functions, couplings between stochastic processes are powerful techniques which have been extensively used to give arigorous foundation to the theory of complex, many component systems and to its many applications in a variety of fields as physics, biology, population dynamics, economics, ... The purpose of the book is to make theseand other mathematical methods accessible to readers with a limited background in probability and physics by examining in detail a few models where the techniques emerge clearly, while extra difficulties arekept to a minimum. Lanford's method and its extension to the hierarchy of equations for the truncated correlation functions, the v-functions, are presented and applied to prove the validity of macroscopic equations forstochastic particle systems which are perturbations of the independent and of the symmetric simple exclusion processes. Entropy inequalities are discussed in the frame of the Guo-Papanicolaou-Varadhan technique and of theKipnis-Olla-Varadhan super exponential estimates, with reference to zero-range models. Discrete velocity Boltzmann equations, reaction diffusion equations and non linear parabolic equations are considered, as limits of particles models. Phase separation phenomena are discussed in the context of Glauber+Kawasaki evolutions and reaction diffusion equations. Although the emphasis is onthe mathematical aspects, the physical motivations are explained through theanalysis of the single models, without attempting, however to survey the entire subject of hydrodynamical limits.".
- catalog contributor b3566031.
- catalog contributor b3566032.
- catalog created "c1991.".
- catalog date "1991".
- catalog date "c1991.".
- catalog dateCopyrighted "c1991.".
- catalog description "Entropy inequalities, correlation functions, couplings between stochastic processes are powerful techniques which have been extensively used to give arigorous foundation to the theory of complex, many component systems and to its many applications in a variety of fields as physics, biology, population dynamics, economics, ... The purpose of the book is to make theseand other mathematical methods accessible to readers with a limited background in probability and physics by examining in detail a few models where the techniques emerge clearly, while extra difficulties arekept to a minimum. Lanford's method and its extension to the hierarchy of equations for the truncated correlation functions, the v-functions, are presented and applied to prove the validity of macroscopic equations forstochastic particle systems which are perturbations of the independent and of the symmetric simple exclusion processes. Entropy inequalities are discussed in the frame of the Guo-Papanicolaou-Varadhan technique and of theKipnis-Olla-Varadhan super exponential estimates, with reference to zero-range models. Discrete velocity Boltzmann equations, reaction diffusion equations and non linear parabolic equations are considered, as limits of particles models. Phase separation phenomena are discussed in the context of Glauber+Kawasaki evolutions and reaction diffusion equations. Although the emphasis is onthe mathematical aspects, the physical motivations are explained through theanalysis of the single models, without attempting, however to survey the entire subject of hydrodynamical limits.".
- catalog description "Includes bibliographical references.".
- catalog extent "196 p. :".
- catalog hasFormat "Mathematical methods for hydrodynamic limits.".
- catalog identifier "0387550046 (New York : alk. paper) :".
- catalog identifier "3540550046 (Berlin : alk. paper) :".
- catalog isFormatOf "Mathematical methods for hydrodynamic limits.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1501.".
- catalog isPartOf "Lecture notes in mathematics ; 1501".
- catalog issued "1991".
- catalog issued "c1991.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog relation "Mathematical methods for hydrodynamic limits.".
- catalog subject "5105 530.1/3 20".
- catalog subject "Distribution (Probability theory).".
- catalog subject "Mathematics.".
- catalog subject "Percolation (Statistical physics)".
- catalog subject "QA3 .L28 no.1501 QC174.85.P45".
- catalog subject "Statistical physics.".
- catalog title "Mathematical methods for hydrodynamic limits / Anna de Masi, Errico Presutti.".
- catalog type "text".