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arXiv · 1801.02520

On the Szeg\H{o} formulas for truncated Wiener-Hopf operators

Alexander V. Sobolev
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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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Alexander V. Sobolev. 2018-01-08. On the Szeg\H{o} formulas for truncated Wiener-Hopf operators. https://doi.org/10.1007/s00020-018-2500-4

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