We derive a general formula for computing the expected first return time of a random walk on a finite graph. Using this framework, we calculate the expected first return time in various settings over bounded rectangular grids with different boundary conditions.
@article{arxiv.2505.00641,
title = {Expected First Return Times for Random Walks on Bounded Grids},
author = {Nan An},
journal= {arXiv preprint arXiv:2505.00641},
year = {2025}
}