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Alain-Sol Sznitman Topics in Occupation Times and Gaussian Free Fields

This set of notes explores some of the links between occupation times and Gaussian processes. Notably they bring into play certain isomorphism theorems going back to Dynkin [4], [5] as well as certain Poisson point processes of Markovian loops, which originated in physics through thework of Symanzik [26]. More recently such Poisson gases of Markovian loops have reappeared in the context of the “Brownian loop soup” of Lawler andWerner [16] and are related to the so-called “random interlacements”, see Sznitman [27]. In particular they have been extensively investigated by Le Jan [17], [18] | Zurich Lectures in Advanced Mathematics Edited by Erwin Bolthausen Managing Editor Freddy Delbaen Thomas Kappeler Managing Editor Christoph Schwab Michael Struwe Gisbert Wustholz Mathematics in Zurich has a long and distinguished tradition in which the writing of lecture notes volumes and research monographs plays a prominent part. The Zurich Lectures in Advanced Mathematics series aims to make some of these publications better known to a wider audience. The series has three main constituents lecture notes on advanced topics given by internationally renowned experts graduate text books designed for the joint graduate program in Mathematics of the ETH and the University of Zurich as well as contributions from researchers in residence at the mathematics research institute FIM-ETH. Moderately priced concise and lively in style the volumes of this series will appeal to researchers and students alike who seek an informed introduction to important areas of current research. Previously published in this series Yakov B. Pesin Lectures on partial hyperbolicity and stable ergodicity Sun-Yung Alice Chang Non-linear Elliptic Equations in Conformal Geometry Sergei B. Kuksin Randomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensions Pavel Etingof Calogero-Moser systems and representation theory Guus Balkema and Paul Embrechts High Risk Scenarios and Extremes - A geometric approach Demetrios Christodoulou Mathematical Problems of General Relativity I Camillo De Lellis Rectifiable Sets Densities and Tangent Measures Paul Seidel Fukaya Categories and Picard-Lefschetz Theory Alexander H.W. Schmitt Geometric Invariant Theory and Decorated Principal Bundles Michael Farber Invitation to Topological Robotics Alexander Barvinok Integer Points in Polyhedra Christian Lubich From Quantum to Classical Molecular Dynamics Reduced Models and Numerical Analysis Shmuel Onn Nonlinear Discrete Optimization - An Algorithmic Theory Kenji Nakanishi and Wilhelm Schlag Invariant