期刊
COMMUNICATIONS IN MATHEMATICAL PHYSICS
卷 376, 期 1, 页码 521-554出版社
SPRINGER
DOI: 10.1007/s00220-019-03625-y
关键词
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We consider Berezin-Toeplitz operators on compact Kahler manifolds whose symbols are characteristic functions. When the support of the characteristic function has a smooth boundary, we prove a two-term Weyl law, the second term being proportional to the Riemannian volume of the boundary. As a consequence, we deduce the area law for the entanglement entropy of integer quantum Hall states. Another application is for the determinantal processes with correlation kernel the Bergman kernels of a positive line bundle: we prove that the number of points in a smooth domain is asymptotically normal.
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