Description 
1 online resource 
Series 
Grundlehren der mathematischen Wissenschaften, 00727830 ; 345 

Grundlehren der mathematischen Wissenschaften ; 345

Contents 
Part 1. General Theory  A WarmingUp Example  Central Limit Theorems  Random Walks in Random Environment  Bounds and Variational Principles for the Asymptotic Variance  Part 2. Simple Exclusion Processes  The Simple Exclusion Process  Selfdiffusion  Equilibrium Fluctuations of the Density Field  Regularity of the Asymptotic Variance  Part 3. Diffusions in Random Environments  Diffusions in Random Environments  Variational Principles for the Limiting Variance  Diffusions with Divergence Free Drifts  Diffusions with Gaussian Drifts  OrnsteinUhlenbeck Process with a Random Potential  Analytic Methods in Homogenization Theory 
Summary 
Diffusive 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 
Analysis 
Distribution (Probability theory) 

Probability Theory and Stochastic Processes 

Mathematical Physics 
Bibliography 
Includes bibliographical references and index 
Subject 
Markov processes.


Fluctuations (Physics)


Martingales (Mathematics)


Markov Chains.

Form 
Electronic book

Author 
Landim, Claudio, 1965


Olla, Stefano, 1959

ISBN 
364229880X (electronic bk.) 

9783642298806 (electronic bk.) 
