Today we finished up talking about G(n,p) and then started our discussion of heavy-tails.
With respect to G(n,p), the main point today was to give you an example of how to use concentration inequalities (e.g., Markov's and Chebychev's) to prove strong threshold results, i.e., threshold results about the probability of an event occurring rather than just about the expectation of an event. Hopefully, you followed along because you'll have to do it for yourself on HW2.
With respect to heavy-tails, we just got started. We're going to talk a lot about heavy-tails next time. This time, we really only talked about what they are, mainly through giving examples. Next time, we'll talk about where they come from. I'll try to give you a glimpse at what is really a whole advanced course in applied probability....
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