Year: 2026
Type: article
Abstract: 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 $$k^{(4-4p)/(3-4p)}$$ k ( 4 - 4 p ) / ( 3 - 4 p ) 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.
Source: Journal of Statistical Physics
Author: Zheng Fang
Institution: University of Zurich
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4417077717
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