Suppose I have a random walker on a 2-d square lattice with periodic boundary conditions with equal probability of going in any of the four directions. The walk ends when the walker reaches the point it started from. What will be the average number of sites visited as a function of the no of steps N taken by such a walker. Can I get an easy bound on this function? Also note, this is not a self avoiding walker. Also, will the properties change if I have a 2-d triangular lattice instead?
2026-03-26 03:01:35.1774494095
Average number of steps to return to the origin of a random walk on a 2-d lattice.
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