Lecture 5

Today we talked a LOT about heavy-tails...and we managed to finish it off, despite the fire alarm!

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 to take away about heavy-tails are the following:
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. (And be sure to look at the details of the proof for Preferential attachment, since that'll be useful on the HW.)

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