#20. Walking in the Yard

Published

27 Nov, 2023

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Prompts for discussion:

  1. Define a \(\ell\)-safe walk to be a walk that involves stepping out of the safe region at most \(\ell\) times (where stepping out involves going out of the safe region and coming back into the safe region in the very next step). The theorem we saw was for \(\ell\)-safe walks with \(d = 0\). For \(d = 1\), can we prove a similar result with a smaller safe region?

  2. It would be nice to find out about the improved bounds known in two dimensions.