The k-extraction Elephant Random Walk is shown to be a Hill-Lane-Sudderth urn, with a phase transition at p=5/6 for k=3, giving initial-condition-dependent limits and a sub-linear entropy region.
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Elephant Random Walk with multiple extractions
The k-extraction Elephant Random Walk is shown to be a Hill-Lane-Sudderth urn, with a phase transition at p=5/6 for k=3, giving initial-condition-dependent limits and a sub-linear entropy region.