Self-avoiding random walks

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I will give a survey talk about two models: the self-avoidng walk and the loop-erased random walk and in doing so will also discuss the problem of simple random walk intersections. The behavior of the walks depends highly on the dimension of the walks. These problems have been a major focus of my research for many years (in some sense, for my entire research career), and I will state what is conjectured, what is known now rigorously, and what still remains as major open questions.

Лекция прочитана в рамках St. Petersburg School in Probability and Statistical Physics.

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