LEADER 03806nam 2200601 450 001 996466474403316 005 20220906120228.0 010 $a3-540-46636-3 024 7 $a10.1007/BFb0086457 035 $a(CKB)1000000000437102 035 $a(SSID)ssj0000324683 035 $a(PQKBManifestationID)12117818 035 $a(PQKBTitleCode)TC0000324683 035 $a(PQKBWorkID)10320413 035 $a(PQKB)10312042 035 $a(DE-He213)978-3-540-46636-9 035 $a(MiAaPQ)EBC5594480 035 $a(Au-PeEL)EBL5594480 035 $a(OCoLC)1076256806 035 $a(MiAaPQ)EBC6841918 035 $a(Au-PeEL)EBL6841918 035 $a(PPN)155218832 035 $a(EXLCZ)991000000000437102 100 $a20220906d1991 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical methods for hydrodynamic limits /$fAnna de Masi, Errico Presutti 205 $a1st ed. 1991. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer,$d[1991] 210 4$dİ1991 215 $a1 online resource (VIII, 196 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1501 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-55004-6 320 $aIncludes bibliographical references. 327 $aHydrodynamic limits for independent particles -- Hydrodynamics of the zero range process -- Particle models for reaction-diffusion equations -- Particle models for the Carleman equation -- The Glauber+Kawasaki process -- Hydrodynamic limits in kinetic models -- Phase separation and interface dynamics -- Escape from an unstable equilibrium -- Estimates on the V-functions. 330 $aEntropy inequalities, correlation functions, couplings between stochastic processes are powerful techniques which have been extensively used to give arigorous foundation to the theory of complex, many component systems and to its many applications in a variety of fields as physics, biology, population dynamics, economics, ... The purpose of the book is to make theseand other mathematical methods accessible to readers with a limited background in probability and physics by examining in detail a few models where the techniques emerge clearly, while extra difficulties arekept to a minimum. Lanford's method and its extension to the hierarchy of equations for the truncated correlation functions, the v-functions, are presented and applied to prove the validity of macroscopic equations forstochastic particle systems which are perturbations of the independent and of the symmetric simple exclusion processes. Entropy inequalities are discussed in the frame of the Guo-Papanicolaou-Varadhan technique and of theKipnis-Olla-Varadhan super exponential estimates, with reference to zero-range models. Discrete velocity Boltzmann equations, reaction diffusion equations and non linear parabolic equations are considered, as limits of particles models. Phase separation phenomena are discussed in the context of Glauber+Kawasaki evolutions and reaction diffusion equations. Although the emphasis is onthe mathematical aspects, the physical motivations are explained through theanalysis of the single models, without attempting, however to survey the entire subject of hydrodynamical limits. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1501. 606 $aPercolation (Statistical physics) 615 0$aPercolation (Statistical physics) 676 $a530.13 700 $aDe Masi$b Anna$f1953-$059538 702 $aPresutti$b Errico$f1942- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466474403316 996 $aMathematical Methods for Hydrodynamic Limits$9382685 997 $aUNISA