Proposition 4.4 . [00AB]

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Proposition 4.4.

Given small numbers $0<\lambda,\kappa\ll 1$ , then for $\delta,\epsilon,t$ sufficiently small depending on $\lambda$ and $\kappa$ , the function $\phi_{CY,t}$ is near its minimum with large probability:

d\mu_{t}(\{\phi_{CY,t}-\min_{X_{t}}\phi_{CY,t}\geq\kappa/5\})<\lambda.