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Alon–Krivelevich–Vu conjecture on concentration of non-extremal eigenvalues
Alon–Krivelevich–Vu conjecture. $\lambda_k(X)$ should be concentrated at least as strongly as $\lambda_1(X)$ .
Conjectureopeneigenvalue-concentration probability random-matricesarXiv posted 2 days ago

Alon–Krivelevich–Vu conjecture on concentration of non-extremal eigenvalues