Lecture 4

Today we talked a LOT about heavy-tails.

The details of what we covered could fill a whole probability course, so don't worry if you don't feel that you could prove all the results -- focus on understanding the intuition behind what I told you.  (And if you want to learn more, ask me and I'll point you in the right direction.)

In my mind the key things from today are
1) Know some examples of heavy-tailed distributions (Pareto, Weibull, and LogNormal)
2) Know some generic processes that create heavy-tails -- additive process (generalized CLT), extremal processes, and multiplicative processes.
3) Know how to apply these ideas to networks in order to get a heavy-tailed degree distribution.  (We introduced Preferential attachment today, and I'll do the proof of the degree distribution next time.)

Like I said in class, I could go on-and-on about heavy-tails...  So, I probably tried to pack too much into 1 lecture.  You'll likely need to go back and look at the notes (which will be up soon) in order to really process everything we talked about.