The Unreasonable Effectiveness of Martingales

I will illustrate the effectiveness of Martingales and stopping times with four examples, involving waiting times for patterns in coin tossing, random graphs, mixing of random walks, and metric space embedding. A common theme is the way stopping time arguments often circumvent the wasteful "union bound" (bounding of the probability of a union by the sum of the individual probabilities).

Yuval Peres, Microsoft Research

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