A coordinate-wise elephant random walk on the hypercube has memory biases that vanish almost surely when p_i < 1, yielding limit theorems whose variance is independent of all memory parameters.
Functional limit theorems for the multi-dimensional elephant ran- dom walk
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Coordinate-wise Elephant Random Walk
A coordinate-wise elephant random walk on the hypercube has memory biases that vanish almost surely when p_i < 1, yielding limit theorems whose variance is independent of all memory parameters.