John-von-Neumann Vorlesung: Simple random walks and random interlacements

Vorlesung:
Termine:

Dienstags, 14:00 bis 17:00 Uhr, Raum 2.01.11 (Tutorraum 2) im Parkring 11 in Garching-Hochbrück

Beginn: 04.12.2012

Dozent:Prof. Dr. Serguei Popov
Inhalt:

1. Simple random walk (SRW), basic facts: recurrence and transience, asymptotic behavior of the Green's function.
2. Potential theory for transient SRW, capacity, recurrent sets. Methods for estimating the capacity of finite sets.
3. Construction of random interlacements (RI); ergodicity and characterization of the RI measure on finite sets.
4. Decoupling inequalities for RI.
5. Interlacement set: connectedness properties, internal distance.
6. Vacant set: percolation.
7. Open problems.

Sprache:Englisch
Literatur:

E.B. Dynkin, A.A. Yushkevich. Markov processes; theorems and problems. Plenum Press, 1969.
G.F. Lawler, V. Limic. Random walk: a modern introduction. Cambridge University Press, 2010.
A.-S. Sznitman. Vacant set of random interlacements and percolation. Ann. of Math. (2), 171(3):2039-2087, 2010.

Skript:-
Prüfung:

Klausur (schriftlich), Dauer: 60 Minuten

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