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Published online by Cambridge University Press: 30 March 2001
For non-uniformly hyperbolic maps of the interval with exponential decay of correlations we prove that the law of closest return to a given point when suitably normalized is almost surely asymptotically exponential. A similar result holds when the reference point is the initial point of the trajectory. We use the framework for non-uniformly hyperbolic dynamical systems developed by L. S. Young.