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Suppose I have random variables $X_1, X_2,...,X_n \in \mathcal{H}$, where $ \mathcal{H}$ is some Hilbert space. How can I bound the following term -

$ P(\| \sum_{i = 1}^n X_i - E[X_i] \|_{\mathcal{H}} \geq \epsilon) $.

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Pages 53, 54 in Gabor's Lugosi slides from a while ago give the answer.

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