Hi, I am interested in the distribution of return times in simple random walks on finite graphs.

Let $G$ be a connected finite graph with, with two independent random walks. If both random walks start are at time $t_0$ on the same node in the graph, how long does it take until they meet again? I have not found papers on this specific problem, but read that is can be transformed to a single random walk and the question of when the random walk returns to exactly the node where it is at $t_0$.

As such I am interested in the distribution of these return times. Generally I know how to compute the numeric values of the distribution for a given graph. But my question is whether this can be modeled through a given distribution (e.g. exponential).

Besides the PDF I am more interested in the CDF of this return time distribution.

reversiblerandom walk with uniform stationary distribution. $\endgroup$4more comments