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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.

3 votes

x-th moment method

Not that I have ever seen this used anywhere (so this might be the wrong direction), but since the second moment method is essentially using Cauchy–Schwarz on the variable $X=X 1_{X>0}$, can't we use …
Bergerac's user avatar