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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.

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extensions to Bernstein's inequality I could use for bounding probability of a union?

I have a set of dependent Bernoulli variables $X_i$ for $i \le N$, with probability $\epsilon$ for the event $X_i=1$. I want to bound the probability that $\sup_i X_i \ge 1$, i.e., I want to know wha …