科研之友
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摘要
We investigate the eigenvalue density in ensembles of large sparse Bernoulli random matrices. Analyzing in detail the spectral density of ensembles of linear subgraphs, we discuss its ultrametric nature and show that near the spectrum boundary, the tails of the spectral density exhibit a Lifshitz singularity typical for Anderson localization. We pay attention to an intriguing connection of the spectral density to the Dedekind eta-function. We conjecture that ultrametricity emerges in rare-event statistics and is inherit to generic complex sparse systems.
- 出版日期2016-1-22
