For free-fermion determinantal processes associated with Berezin-Toeplitz operators, smooth linear statistics satisfy a two-term Szegő-type expansion and a Gaussian CLT with variance equal to half the H1 seminorm in the bulk plus a flow-dependent H1/2 seminorm on the boundary.
Fluctuations of eigenvalues of random normal matrices
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Fluctuations of two-dimensional determinantal processes associated with Berezin--Toeplitz operators
For free-fermion determinantal processes associated with Berezin-Toeplitz operators, smooth linear statistics satisfy a two-term Szegő-type expansion and a Gaussian CLT with variance equal to half the H1 seminorm in the bulk plus a flow-dependent H1/2 seminorm on the boundary.