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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
8
votes
Probability in number theory
Statistical Independence in Probability, Analysis, and Number Theory, by Mark Kac -- an amazingly potent piece of mathematical writing given its rather minuscule size. While now slightly out of date …
2
votes
Accepted
Football Squares
Alternative (and rough) idea for a model: Consider a random walk on score vectors $[x,y]$ where x and y represent the scores of the two teams. Set $P_0=[0,0]$. Let $P_1=P_0+v_1$ where $v_1$ is with …
1
vote
Risk dice roll probabilities
You should use as many dice as possible while defending (so always 2, unless you have one army).
This problem has no doubt been tackled by hundreds of probability students over the years, and it is …