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- W4367000514 abstract "We consider the determinantal point processes associated with the spectral projectors of a Schrodinger operator on $mathbb{R}$, with a smooth confining potential. In the semiclassical limit, where the number of particles tends to infinity, we obtain a SzegH{o}-type central limit theorem (CLT) for the fluctuations of smooth linear statistics. More precisely, the Laplace transform of any statistic converges without renormalization to a Gaussian limit with a $H^{1/2}$-type variance, which depends on the potential. In the one-well (one-cut) case, using the quantum action-angle theorem and additional micro-local tools, we reduce the problem to the asymptotics of Fredholm determinants of certain approximately Toeplitz operators. In the multi-cut case, we show that for generic potentials, a similar result holds and the contributions of each wells are independent in the limit." @default.
- W4367000514 created "2023-04-27" @default.
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- W4367000514 date "2023-04-24" @default.
- W4367000514 modified "2023-09-29" @default.
- W4367000514 title "Central limit theorem for smooth statistics of one-dimensional free fermions" @default.
- W4367000514 doi "https://doi.org/10.48550/arxiv.2304.12275" @default.
- W4367000514 hasPublicationYear "2023" @default.
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