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- W2912449603 abstract "The total-variation cutoff phenomenon for simple random walk has been conjectured to apply to all transitive expanders. However, very little is actually known regarding this conjecture and cutoff on sparse graphs in general. In this paper we prove that simple random walk on Ramanujan complexes of type $tilde{A}_{d}$ ($dgeq1$) exhibit total-variation cutoff, thereby extending the case of regular Ramanujan graphs ($d=1$). As a consequence we obtain explicit generators for $PGL_{d}(mathbb{F}_{q})$ for which the associated Cayley graphs exhibit total-variation cutoff." @default.
- W2912449603 created "2019-02-21" @default.
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- W2912449603 date "2019-01-27" @default.
- W2912449603 modified "2023-09-27" @default.
- W2912449603 title "Cutoff on Ramanujan Complexes" @default.
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