000 04246nam a22004935i 4500
001 978-3-642-29880-6
003 DE-He213
005 20140220083317.0
007 cr nn 008mamaa
008 120705s2012 gw | s |||| 0|eng d
020 _a9783642298806
_9978-3-642-29880-6
024 7 _a10.1007/978-3-642-29880-6
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aKomorowski, Tomasz.
_eauthor.
245 1 0 _aFluctuations in Markov Processes
_h[electronic resource] :
_bTime Symmetry and Martingale Approximation /
_cby Tomasz Komorowski, Claudio Landim, Stefano Olla.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2012.
300 _aXVII, 491 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v345
505 0 _aPreface -- Part I: General Theory -- 1.A Warming-up Example -- 2.Central Limit Theorems -- 3.RandomWalks in Random Environment -- 4.Bounds and Variational Principles for the Asymptotic Variance -- Part II: Simple Exclusion Processes -- 5.The Simple Exclusion Process -- 6.Self Diffusion -- 7.Equilibrium Fluctuations of the Density Field -- 8.Regularity of the Asymptotic Variance -- Part III: Diffusions in Random Environments -- 10.Variational Principles for the Limiting Variance -- 11.Diffusions with Divergence Free Drifts -- 12.Diffusions with Gaussian Drifts -- 13.Ornstein-Uhlenbeck Process with a Random Potential -- 14.Analytic Methods in Homogenization Theory -- References -- Notation -- Subject Index.
520 _aDiffusive phenomena in statistical mechanics and in other fields arise from markovian modeling and their study requires sophisticated mathematical tools. In infinite dimensional situations, time symmetry properties can be exploited in order to make martingale approximations, along the lines of the seminal work of Kipnis and Varadhan. The present volume contains the most advanced theories on the martingale approach to central limit theorems. Using the time symmetry properties of the Markov processes, the book develops the techniques that allow us to deal with infinite dimensional models that appear in statistical mechanics and engineering (interacting particle systems, homogenization in random environments, and diffusion in turbulent flows, to mention just a few applications). The first part contains a detailed exposition of the method, and can be used as a text for graduate courses. The second concerns application to exclusion processes, in which the duality methods are fully exploited. The third part is about the homogenization of diffusions in random fields, including passive tracers in turbulent flows (including the superdiffusive behavior).   There are no other books in the mathematical literature that deal with this kind of approach to the problem of the central limit theorem. Hence, this volume meets the demand for a monograph on this powerful approach, now widely used in many areas of probability and mathematical physics. The book also covers the connections with and application to hydrodynamic limits and homogenization theory, so besides probability researchers it will also be of interest to mathematical physicists and analysts.
650 0 _aMathematics.
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aMathematical Physics.
700 1 _aLandim, Claudio.
_eauthor.
700 1 _aOlla, Stefano.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642298790
830 0 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v345
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-29880-6
912 _aZDB-2-SMA
999 _c103102
_d103102