This graduate textbook provides a detailed introduction to the
probabilistic interpretation of nonlinear potential theory, relying
on the recently introduced notion of tug-of-war games with
noise.The book explores both basic and more advanced constructions,
carefully explaining the parallel between linear and nonlinear
cases. The presentation is self-contained with many exercises,
making the book suitable as a textbook for a graduate course, as
well as for self-study. Extensive background and auxiliary material
allow the tailoring of courses to individual student levels.
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