This book presents the lecture notes and articles from the workshop on hydrodynamic limits held at The Fields Institute (Toronto). The first part of the book contains the notes from the mini-course given by Professor S. R. S. Varadhan. The second part contains research articles reviewing the diverse progress in the study of hydrodynamic limits and related areas. This book offers a comprehensive introduction to the theory and its techniques, including entropy and relative entropy methods, large deviation estimates, and techniques in nongradient systems. This book, especially the lectures of Part I, could be used as a text for an advanced graduate course in hydrodynamic limits and interacting particle systems.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Graduate students and research mathematicians interested in interacting particle systems, hydrodynamic limits, and statistical mechanics.

Table of Contents

• S. R. S. Varadhan -- Lectures on hydrodynamic scaling

• J. A. Carrillo -- On a 1-d granular media immersed in a fluid
• H. Fukś -- A class of cellular automata equivalent to deterministic particle systems
• T. Funaki -- Recent results on the Ginzburg-Landau \(\nabla\phi\) interface model
• I. Grigorescu -- Large scale behavior of a system of interacting diffusions
• R. Illner -- Stellar dynamics and plasma physics with corrected potentials: Vlasov, Manev, Boltzmann, Smoluchowski
• J. Quastel -- Free boundary problem and hydrodynamic limit
• T. Seppäläinen -- A variational coupling for a totally asymmetric exclusion process with long jumps but no passing
• H.-T. Yau -- Quantum mechanics, linear Boltzmann equation and renormalization