John von Neumann Gastvorlesung

Title: Random walk in random environment

Lecture Dates: Wednesdays, 14:00 to 16:00 in room BC1 2.02.11, Seminarraum at Parkring 11-13 in Garching-Hochbrück.
First Lecture: December 5, 2018
Instructor: Prof. Dr. Alejandro Ramírez
 

Program:
I. General properties:
(i) The environment seen from the random walk and its invariant measures.
(iii) Transience and recurrence in dimension d=1.
(iv) Kozlov's theorem.
(v) Balanced random walks in random environment.

II. Ballisticity conditions
(i) Relations between directional transience and ballisticity.
(ii) Ballisticity conditions and renormalization methods.
(iii) Random walk at low disorder.

III. Random walk in random environment, directed polymers and the KPZ universality class
(i) Large deviations and equality of the quenched and annealed rate functions
(ii) Relation with random polymers
(iii) KPZ in random walk at weak disorder.
(iv) Exactly solvable directed random walks in random environment.

Bibliografy: 1. Drewitz, Alexander; Ramírez, Alejandro F. Selected topics in random walks in random environment. Topics in percolative and disordered systems, 23–83, Springer Proc. Math. Stat., 69, Springer, New York, (2014). 2. Sznitman, Alain-Sol. Topics in random walks in random environment. School and Conference on Probability Theory, 203–266, ICTP Lect. Notes, XVII, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2004.