Today we had what basically turned into a probability lecture about heavy-tailed distribution. We spent the time talking about (i) some examples of heavy-tailed distributions and properties of them and (ii) what processes lead to heavy tails. Then, we applied what we learned about where heavy-tails come from to the context of graphs to give a simple model (preferential attachment) that leads to heavy-tailed degree distributions.

During the second part, we talked about some very deep probability results (generalized central limit theorem and extreme value theory) where I gave only a peek of the results. If you're interested in learning more about these, let me know and I'll point you to some references.

(The notes will go on the course webpage by the end of the day.)

## Wednesday, January 20, 2010

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