An Introduction to Random Interlacements

• Main Authors: Drewitz, Alexander (Author), Ráth, Balázs (Author), Sapozhnikov, Artëm (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Series: SpringerBriefs in Mathematics,
• Subjects: Mathematics.; Applied mathematics.; Engineering mathematics.; Operations research.; Management science.; Probabilities.; Probability Theory and Stochastic Processes.; Operations Research, Management Science.; Applications of Mathematics.

This book gives a self-contained introduction to the theory of random interlacements. The intended reader of the book is a graduate student with a background in probability theory who wants to learn about the fundamental results and methods of this rapidly emerging field of research. The model was i...

Table of Contents:

• Random Walk, Green Function, Equilibrium Measure
• Random Interlacements: First Definition and Basic Properties.- Random Walk on the Torus and Random Interlacements.- Poisson Point Processes.- Random Interlacements Point Process.- Percolation of the Vacant Set.- Source of Correlations and Decorrelation via Coupling.- Decoupling Inequalities
• Phase Transition of Vu
• Coupling of Point Measures of Excursions.