## Random Walk anecdote.

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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 2010 at 4:38

## 2 Answers

The anecdote is about Polya, and it is in his contribution, Two incidents, to the book, Scientists at Work: Festschrift in Honour of Herman Wold, edited by T Dalenius, G Karlsson, and S Malmquist, published in Sweden in 1970. It was recently quoted on page 229 of David A Levin and Yuval Peres, Polya's Theorem on random walks via Polya's Urn, Amer Math Monthly 117 (March, 2010) 220-231.

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Thank you. This is exactly what I was looking for. – Ross Snider Apr 21 2010 at 4:55

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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 $d>2$.

Here you can find a reference to the anecdote: http://m759.xanga.com/122558830/item/

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1
Ahh, in fact I do plan to use this in the article (I already knew the quote and its author). The article is about the number three and where it shows up as a transition point to more interesting and complex behavior. You know, like the 3-body problem, 3-dimension random walks, 3-colorings of planar maps, 3-SAT and NP-Completeness, FLT, or 3 bubble conjecture. I would post on MO for more but I have a suspicion the question would not be received well. As for this answer, it isn't quite an anecdote, although fantastic nevertheless. – Ross Snider Apr 21 2010 at 13:43
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