The conjecture bears on the estimation of the frequencies of a round drum or, in mathematical terms, the eigenvalues of a disk. Pólya himself confirmed his conjecture in 1961 for domains that ...

Rui Peng, Maolin Zhou, Effects of Large Degenerate Advection and Boundary Conditions on the Principal Eigenvalue and its Eigenfunction of A Linear Second-Order Elliptic Operator, Indiana University ...

The Annals of Statistics, Vol. 48, No. 6 (December 2020), pp. 3138-3160 (23 pages) This paper studies the joint limiting behavior of extreme eigenvalues and trace of large sample covariance matrix in ...