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prob.part12.25_26

# prob.part12.25_26 - 1.1 SIMULATION OF DISCRETE...

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1.1. SIMULATION OF DISCRETE PROBABILITIES 17 At the hotel there lived also some students with whom I usually took my meals and had friendly relations. On a certain day one of them expected the visit of his fianc´ ee, what (sic) I knew, but I did not foresee that he and his fianc´ ee would also set out for a stroll in the woods, and then suddenly I met them there. And then I met them the same morning repeatedly, I don’t remember how many times, but certainly much too often and I felt embarrassed: It looked as if I was snooping around which was, I assure you, not the case. 13 This set him to thinking about whether random walkers were destined to meet. olya considered random walkers in one, two, and three dimensions. In one dimension, he envisioned the walker on a very long street. At each intersec- tion the walker flips a fair coin to decide which direction to walk next (see Figure 1.6a). In two dimensions, the walker is walking on a grid of streets, and at each intersection he chooses one of the four possible directions with equal probability (see Figure 1.6b). In three dimensions (we might better speak of a random climber), the walker moves on a three-dimensional grid, and at each intersection there are now six di ff erent directions that the walker may choose, each with equal probability (see Figure 1.6c).

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