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20 Random Walks - MIT OpenCourseWare

Mcs-ftl 2010/9/8 0:40 page 533 #539. 20 Random Walks Random Walks are used to model situations in which an object moves in a sequence of steps in randomly chosen directions. Many phenomena can be modeled as a Random walk and we will see several examples in this chapter. Among other things, we'll see why it is rare that you leave the casino with more money than you entered with and we'll see how the Google search engine uses Random Walks through the graph of the world-wide web links to determine the relative importance of websites. Unbiased Random Walks A Bug's Life There is a small flea named Stencil. To his right, there is an endless flat plateau. One inch to his left is the Cliff of Doom, which drops to a raging sea filled with flea-eating monsters.

probability 1. And since lim w!1 w n w D1 for any finite n, this is true no matter where Stencil starts. Our little friend is doomed! Hey, you know how in the movies they often make it look like the hero dies, but then he comes back in the end and everything turns out okay? Well, we’re not sayin’ anything, just pointing that out. 20.1.5 ...

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