Consider a random walk on $\mathbb{Z}^2$ which goes forward (i.e. takes a step in the same direction as the last step) with probability $p$ and turns right and left with probability $\frac{1-p}{2}$ respectively. Is it recurrent for all $1 > p \geq 0$?
Random walk on $\mathbb{Z}^2$ going forward with probability $p$
Frederik Ravn Klausen
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