Lecture
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25 Feb 2026 (2h 00m)
ALESSANDRA Caraceni - Course (teaching activity) - Both face to face and online
Intro to random walks on graphs; gambler's ruin, harmonicity and the optional stopping theorem; harmonic functions on a graph; the electrical network setup; Z is recurrent
27 Feb 2026 (2h 00m)
ALESSANDRA Caraceni - Course (teaching activity) - Both face to face and online
The type problem
04 Mar 2026 (2h 00m)
ALESSANDRA Caraceni - Course (teaching activity) - Both face to face and online
Transience and the existence of a finite-energy flow to infinity; rough embeddings.
13 Mar 2026 (2h 00m)
ALESSANDRA Caraceni - Course (teaching activity) - Both face to face and online
The hyperbolic plane is transitive, isoperimetric inequalities, random walks on groups and the type of Cayley graphs.
18 Mar 2026 (2h 00m)
ALESSANDRA Caraceni - Course (teaching activity) - Both face to face and online
Donsker's theorem: RWs and Brownian motion
20 Mar 2026 (2h 00m)
ALESSANDRA Caraceni - Course (teaching activity) - Both face to face and online
Brownian motion and the Dirichlet problem in R^d. Recurrence and transience of Brownian motion.
25 Mar 2026 (2h 00m)
ALESSANDRA Caraceni - Course (teaching activity) - Both face to face and online
Intro to the Gaussian Free Field: the Brownian bridge.
27 Mar 2026 (2h 00m)
ALESSANDRA Caraceni - Course (teaching activity) - Both face to face and online
The DGFF on domains of Z^d and the domain Markov property. The Green function. Sketch of the construction of the GFF on domains of R^d.
01 Apr 2026 (2h 00m)
ALESSANDRA Caraceni - Course (teaching activity) - Both face to face and online
Uniform Spanning Trees. Wilson's algorithm and the LERW.
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