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- W4311001703 abstract "We consider a variant of the configuration model with an embedded community structure and study the mixing properties of a simple random walk on it. Every vertex has an internal $mathrm{deg}^{text{int}}geq 3$ and an outgoing $mathrm{deg}^{text{out}}$ number of half-edges. Given a stochastic matrix $Q$, we pick a random perfect matching of the half-edges subject to the constraint that each vertex $v$ has $mathrm{deg}^{text{int}}(v)$ neighbours inside its community and the proportion of outgoing half-edges from community $i$ matched to a half-edge from community $j$ is $Q(i,j)$. Assuming the number of communities is constant and they all have comparable sizes, we prove the following dichotomy: simple random walk on the resulting graph exhibits cutoff if and only if the product of the Cheeger constant of $Q$ times $log n$ (where $n$ is the number of vertices) diverges. In [4], Ben-Hamou established a dichotomy for cutoff for a non-backtracking random walk on a similar random graph model with 2 communities. We prove the same characterisation of cutoff holds for simple random walk." @default.
- W4311001703 created "2022-12-22" @default.
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- W4311001703 date "2022-12-08" @default.
- W4311001703 modified "2023-10-17" @default.
- W4311001703 title "Cutoff for random walk on random graphs with a community structure" @default.
- W4311001703 doi "https://doi.org/10.48550/arxiv.2212.04469" @default.
- W4311001703 hasPublicationYear "2022" @default.
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