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We prove a special case of a conjecture in asymptotic analysis by HaroldWidom. More precisely, we establish the leading and next-to-leading term of asemi-classical expansion of the trace of the square of certain integraloperators on the Hilbert space $L^2(\R^d)$. As already observed by Gioev andKlich, this implies that the bi-partite entanglement entropy of the free Fermigas in its ground state grows at least as fast as the surface area of thespatially bounded part times a logarithmic enhancement.

A Special Case Of A Conjecture By Widom With Implications To Fermionic Entanglement Entropy