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Martin boundaries and random walks. (English) Zbl 0891.60073
Korányi, Adam (ed.), Harmonic functions on trees and buildings. Workshop on harmonic functions on graphs, New York, NY, October 30–November 3, 1995. Providence, RI: American Mathematical Society. Contemp. Math. 206, 17-44 (1997).
This rather big article can serve as good short survey of the Martin boundary theory for random walks. The paper contains the main classical results of this theory, and gives many examples of their applications.
For the entire collection see [Zbl 0869.00032].

60J50 Boundary theory for Markov processes
60G50 Sums of independent random variables; random walks
31C35 Martin boundary theory
31C05 Harmonic, subharmonic, superharmonic functions on other spaces