{"product_id":"9783540550044","title":"Lecture Notes in Mathematics","description":"\u003ch1\u003eLecture Notes in Mathematics\u003c\/h1\u003e \u003ch2\u003eDeMasi, Anna; Presutti, Errico\u003c\/h2\u003e \u003cp\u003eEntropy inequalities, correlation functions, couplings\nbetween stochastic   processes are powerful techniques which\nhave been extensively used to give arigorous foundation to\nthe theory of complex, many component systems and to its\nmany applications in a variety of fields as physics,\nbiology,       population dynamics, economics, ...\nThe purpose of the book is to make theseand other\nmathematical methods accessible to readers with a                 limited\nbackground in probability and physics by examining in detail\na  few models where the techniques emerge clearly, while\nextra difficulties arekept to a minimum.\nLanford's method and its extension to the hierarchy      of\nequations for the truncated correlation functions, the\nv-functions,  are presented and applied to prove the validity\nof macroscopic equations forstochastic particle systems\nwhich are perturbations of the independent and  of the\nsymmetric simple exclusion processes. Entropy inequalities\nare   discussed in the frame of the Guo-Papanicolaou-Varadhan\ntechnique and of theKipnis-Olla-Varadhan super exponential\nestimates, with reference to         zero-range models. Discrete\nvelocity Boltzmann equations, reaction          diffusion\nequations and non linear parabolic equations are                  considered,\nas limits of particles models. Phase separation                 phenomena\nare discussed in the context of Glauber+Kawasaki                  evolutions\nand reaction diffusion equations. Although the emphasis is\nonthe mathematical aspects, the physical motivations are\nexplained through theanalysis of the single models, without\nattempting, however to survey the    entire subject of\nhydrodynamical limits.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1992-01-15\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783540550044\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/BFb0086457\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 196\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":45369786007692,"sku":"9783540550044","price":35.96,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783540550044.jpg?v=1772802865","url":"https:\/\/lateknightbooks.com\/products\/9783540550044","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}