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"Flows and walks on graphs" by Shmuel Weinberger

Suppose that a bacterium splits in two with probability 1/2 or otherwise dies, and we start with a small colony of 1000 bacteria. Can we expect to obtain an immortal colony? If I randomly walk on a line from a position one unit from my home, and I go in each direction with equal probability, how long will it take me to get home? What about in higher dimensional space? Is it possible to rearrange the assets of the points of a graph through trade among neighbors so that all profit? These are among the problems that I will explain and interrelate in this introduction to the geometric/probabilistic side of graphs.

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