Asymptotic shape of the region visited by an Eulerian walker.


We study an Eulerian walker on a square lattice, starting from an initial randomly oriented background using Monte Carlo simulations. We present evidence that, for a large number of steps N , the asymptotic shape of the set of sites visited by the walker is a perfect circle. The radius of the circle increases as N1/3, for large N , and the width of the… (More)


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@article{Kapri2009AsymptoticSO, title={Asymptotic shape of the region visited by an Eulerian walker.}, author={Rajeev Kapri and Deepak Dhar}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2009}, volume={80 5 Pt 1}, pages={051118} }