We tackle some fundamental problems in probability theory on corrupted random processes on the integer line. We analyze when a biased random walk is expected to reach its bottommost point and when intervals of integer points can be detected under a natural model of noise.

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Abstract

We tackle some fundamental problems in probability theory on corrupted random
processes on the integer line. We analyze when a biased random walk is expected
to reach its bottommost point and when intervals of integer points can be
detected under a natural model of noise. We apply these results to problems in
learning thresholds and intervals under a new model for learning under
adversarial design.