Резюме: We study how conditioning on the first \(k\) steps, which we think of as training, affects the long-term behavior of the Elephant Random Walk. When the elephant is conditioned to be at position \(k\) at time \(k\), the first return time to the origin scales as \(k^{(4−4p)⁄(3−4p)}\) in the diffusive regime, and grows exponentially in the critical regime. We loosely interpret this as a measurement of the rate at which the elephant forgets its training.

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