Outliers in spectrum of sparse Wigner matrices

@article{Tikhomirov2021OutliersIS,
  title={Outliers in spectrum of sparse Wigner matrices},
  author={Konstantin E. Tikhomirov and Pierre Youssef},
  journal={Random Structures \& Algorithms},
  year={2021},
  volume={58},
  pages={517 - 605}
}
In this paper, we study the effect of sparsity on the appearance of outliers in the semi‐circular law. Let (Wn)n=1∞ be a sequence of random symmetric matrices such that each Wn is n × n with i.i.d. entries above and on the main diagonal equidistributed with the product bnξ , where ξ is a real centered uniformly bounded random variable of unit variance and bn is an independent Bernoulli random variable with a probability of success pn. Assuming that limn→∞npn=∞ , we show that for the random… 
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