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We derive some large deviation bounds for events related to the "trueself-repelling motion", a one-dimensional self-interacting process introducedby Toth and Werner, that has very different path properties than usualdiffusion processes. We then use these estimates to study certain of these pathproperties such as its law of iterated logarithms for both small and largetimes.

Large deviations and path properties of the true self-repelling motion