From random walk trajectories to random interlacements. (English) Zbl 1269.60002

Černý, Jiří; Teixeira, Augusto Quadros

Ensaios Matemáticos 23. Rio de Janeiro: Sociedade Brasileira de Matemática (ISBN 978-85-85818-69-2/pbk). 77 p. (2012).

Summary: We review and comment recent research on a random interlacements model introduced by A.-S. Sznitman [Ann. Math. (2) 171, No. 3, 2039–2087 (2010; Zbl 1202.60160)].
A particular emphasis is put on motivating the definition of the model via natural questions concerning geometrical/percolative properties of random walk trajectories on finite graphs, as well as on presenting some important techniques used from the literature on random interlacements in the most accessible way. This text is an expanded version of the lecture notes for a mini-course given at the XV Brazilian School of Probability in 2011.

MSC:

60-02	Research exposition (monographs, survey articles) pertaining to probability theory
60G50	Sums of independent random variables; random walks
60K35	Interacting random processes; statistical mechanics type models; percolation theory
05C81	Random walks on graphs

Keywords:

random interlacements; random walk trajectories on finite graphs; percolation

Citations:

Zbl 1202.60160