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Central limit theorem for spectral partial Bergman kernels

Steve Zelditch and Peng Zhou

Geometry & Topology 23 (2019) 1961–2004
Bibliography
1 R J Berman, Bergman kernels and equilibrium measures for line bundles over projective manifolds, Amer. J. Math. 131 (2009) 1485 MR2559862
2 P Bleher, B Shiffman, S Zelditch, Universality and scaling of correlations between zeros on complex manifolds, Invent. Math. 142 (2000) 351 MR1794066
3 T Can, P J Forrester, G Téllez, P Wiegmann, Singular behavior at the edge of Laughlin states, Phys. Rev. B 89 (2014)
4 L Charles, Berezin–Toeplitz operators, a semi-classical approach, Comm. Math. Phys. 239 (2003) 1 MR1997113
5 I Daubechies, Coherent states and projective representation of the linear canonical transformations, J. Math. Phys. 21 (1980) 1377 MR574700
6 H Delin, Pointwise estimates for the weighted Bergman projection kernel in n, using a weighted L2 estimate for the equation, Ann. Inst. Fourier (Grenoble) 48 (1998) 967 MR1656004
7 M Dimassi, J Sjöstrand, Spectral asymptotics in the semi-classical limit, 268, Cambridge Univ. Press (1999) MR1735654
8 M R Douglas, S Klevtsov, Bergman kernel from path integral, Comm. Math. Phys. 293 (2010) 205 MR2563804
9 G B Folland, Harmonic analysis in phase space, 122, Princeton Univ. Press (1989) MR983366
10 L Hörmander, The analysis of linear partial differential operators, IV : Fourier integral operators, 275, Springer (1985) MR781537
11 N Lindholm, Sampling in weighted Lp spaces of entire functions in n and estimates of the Bergman kernel, J. Funct. Anal. 182 (2001) 390 MR1828799
12 Z Lu, B Shiffman, Asymptotic expansion of the off-diagonal Bergman kernel on compact Kähler manifolds, J. Geom. Anal. 25 (2015) 761 MR3319950
13 X Ma, G Marinescu, Holomorphic Morse inequalities and Bergman kernels, 254, Birkhäuser (2007) MR2339952
14 A Melin, J Sjöstrand, Fourier integral operators with complex-valued phase functions, from: "Fourier integral operators and partial differential equations" (editor J Chazarain), Lecture Notes in Math. 459, Springer (1975) 120 MR0431289
15 L Boutet de Monvel, V Guillemin, The spectral theory of Toeplitz operators, 99, Princeton Univ. Press (1981) MR620794
16 L Boutet de Monvel, J Sjöstrand, Sur la singularité des noyaux de Bergman et de Szegő, from: "Journées : Équations aux dérivées partielles de Rennes", Astérisque 34–35, Soc. Math. France (1976) 123 MR0590106
17 R Paoletti, Scaling asymptotics for quantized Hamiltonian flows, Internat. J. Math. 23 (2012) MR2999047
18 R Paoletti, Local scaling asymptotics in phase space and time in Berezin–Toeplitz quantization, Internat. J. Math. 25 (2014) MR3225584
19 F T Pokorny, M Singer, Toric partial density functions and stability of toric varieties, Math. Ann. 358 (2014) 879 MR3175144
20 D Robert, Autour de l’approximation semi-classique, 68, Birkhäuser (1987) MR897108
21 J Ross, M Singer, Asymptotics of partial density functions for divisors, J. Geom. Anal. 27 (2017) 1803 MR3667411
22 Y A Rubinstein, S Zelditch, The Cauchy problem for the homogeneous Monge–Ampère equation, I : Toeplitz quantization, J. Differential Geom. 90 (2012) 303 MR2899878
23 B Shiffman, S Zelditch, Asymptotics of almost holomorphic sections of ample line bundles on symplectic manifolds, J. Reine Angew. Math. 544 (2002) 181 MR1887895
24 E M Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, 43, Princeton Univ. Press (1993) MR1232192
25 X G Wen, Quantum field theory of many-body systems: from the origin of sound to an origin of light and electrons, Oxford Univ. Press (2004)
26 P Wiegmann, Nonlinear hydrodynamics and fractionally quantized solitons at the fractional quantum Hall edge, Phys. Rev. Lett. 108 (2012)
27 S Zelditch, Index and dynamics of quantized contact transformations, Ann. Inst. Fourier (Grenoble) 47 (1997) 305 MR1437187
28 S Zelditch, P Zhou, Interface asymptotics of partial Bergman kernels on S1–symmetric Kaehler manifolds, preprint (2016) arXiv:1604.06655
29 S Zelditch, P Zhou, Central limit theorem for toric manifolds, preprint (2018) arXiv:1802.08501
30 S Zelditch, P Zhou, Interface asymptotics of partial Bergman kernels around a critical level, preprint (2018) arXiv:1805.01804
31 S Zelditch, P Zhou, Pointwise Weyl law for partial bergman kernels, from: "Algebraic and analytic microlocal analysis" (editors M Hitrik, D Tamarkin, B Tsygan, S Zelditch), Springer Proc. Math. Stat. 269, Springer (2018) 589