Cutoff on graphs and the Sarnak–Xue density of eigenvalues
نویسندگان
چکیده
It was recently shown in Lubetzky and Peres (2016) Sardari (2019) that Ramanujan graphs, i.e., graphs with the optimal spectrum, exhibit cutoff of simple random walk an time have almost-diameter. We show this spectral condition can be replaced by a weaker condition, Sarnak–Xue density property, to deduce similar results. This allows us prove some natural families Schreier SL2Ft-action on projective line cutoff, thus proving special case conjecture Rivin (2019).
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2022
ISSN: ['1095-9971', '0195-6698']
DOI: https://doi.org/10.1016/j.ejc.2022.103530