# Random Walk anecdote.

I'm looking for an anecdote about a mathematician who studied random walks. I'm attempting to write an article and hope to include the story (but only if I can get the details correct). I'll try to do my best describing it in hopes someone else has heard it and knows a name or the full story.

A mathematician was walking through the park and entertaining mathematical whims. He noticed that he kept running into this same couple as he wandered around aimlessly. He wasn't sure if this behaviour was expected by chance or whether perhaps the female of the couple thought that he was cute. He rushed home to analyse the situation in terms of random walks in two dimensions.

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Perhaps you should also add the assumption that the park is compact, because it seems to me that if it isn't and if the couple is not walking randomly, then the probability that the mathematician will run into the couple over and over is not 1. –  Peter Samuelson Apr 21 '10 at 4:38

My favorite is this one attributed to Kakutani: "A drunk man will find his way home, but a drunk bird may get lost forever." referring to the fact that the simple random walk in $Z^2$ is recurrent while it is transient in $Z^d$ for $d>2$.