Abstract
We consider functions of multi-dimensional versions of truncated Wiener–Hopf operators with smooth symbols, and study the scaling asymptotics of their traces. The obtained results extend the asymptotic formulas obtained by H. Widom in the 1980’s to non-smooth functions, and non-smooth truncation domains. The obtained asymptotic formulas are used to analyse the scaling limit of the spatially bipartite entanglement entropy of thermal equilibrium states of non-interacting fermions at positive temperature.
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Acknowledgements
This paper grew out of numerous discussions with H. Leschke and W. Spitzer, who have author’s deepest gratitude. A part of this paper was written during several visits of the author to the FernUniversität Hagen in 2015-2016.
The author was supported by EPSRC grant EP/J016829/1.
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Sobolev, A.V. On Szegő Formulas for Truncated Wiener–Hopf Operators. Integr. Equ. Oper. Theory 91, 1 (2019). https://doi.org/10.1007/s00020-018-2500-4
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DOI: https://doi.org/10.1007/s00020-018-2500-4