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Imagine a man coming out of a bar in cancun, an open bottle of sunscreen dribbling from his back pocket. He walks forward for a few steps, and then there’s a good chance that he will stumble in one direction or another. He steadies himself, takes another step, and then stumbles once again. the direction in which the man stumbles is basically random, at least insofar as it has nothing to do with his purported destination. If the man stumbles o en enough, the path traced by the sunscreen dripping on the ground as he weaves his way back to his hotel (or just as likely in another direction entirely) will look like the path of a dust particle oating in the sunlight. […]
Imagine that the drunkard from cancun is now back at his hotel. He gets out of the elevator and is faced with a long hallway, stretching to both isle and his right. At one end of the hallway is room 700; at the other end is room 799. He is somewhere in the middle, but he has no idea which way to go to get to his room. He stumbles to and fro, half the time moving one way down the hall, and half the time moving in the opposite direction. Here’s the question that the mathematical theory of random walks allows you to answer: Suppose that with each step the drunkard takes, there is a 50% chance that that step will take him a little further toward room 700, at one end of the long hallway, and a 50% chance that it will take him a little further toward room 799, at the other end. What is the probability that, a er one hundred steps, say, or a thousand steps, he is standing in front of a given room?
The Physics of Wall Street by Weatherall
For a nice description see chapter 23 and 24 in Sleeping Beauties in Theoretical Physics by Thanu Padmanabhan