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Poisson occupancy of paths on permuted regular graphs
In the classical occupancy problem, $B$ balls are placed independently and uniformly into $d$ boxes. We study a graph analogue of this model. Let $G$ be a directed $r$-regular graph on $d$ vertices and fix a vertex $i$. Consider all paths of length $L$ starting from $i$, and let $N_L(i,j)$ denote th
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