The sparse circular law under minimal assumptions

  title={The sparse circular law under minimal assumptions},
  author={Mark Rudelson and Konstantin E. Tikhomirov},
  journal={Geometric and Functional Analysis},
The circular law asserts that the empirical distribution of eigenvalues of appropriately normalized $${n \times n}$$n×n matrix with i.i.d. entries converges to the uniform measure on the unit disc as the dimension n grows to infinity. Consider an $${n \times n}$$n×n matrix $${A_n=(\delta_{ij}^{(n)}\xi_{ij}^{(n)})}$$An=(δij(n)ξij(n)), where $${\xi_{ij}^{(n)}}$$ξij(n) are copies of a real random variable of unit variance, variables $${\delta_{ij}^{(n)}}$$δij(n) are Bernoulli (0/1) with $${\mathbb… 
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