Full Szegő-type trace asymptotics for ergodic operators on large boxes

Abstract

We prove full Szegő-type large-box trace asymptotics for selfadjoint ${\mathbb{Z}}^d$-ergodic operators $\Omega \ni \omega \mapsto H_{\omega }$ acting on $L^2({\mathbb{R}}^d)$. More precisely, let $g$ be a bounded, compactly supported and real-valued function such that the (averaged) operator kernel of $g(H_{\omega })$ decays sufficiently fast, and let $h$ be a sufficiently smooth compactly supported function. We then prove a full asymptotic expansion of the averaged trace of the operator $h(g(H_{\omega }{)}_{[-L,L{]}^d})$ in terms of the length-scale $L$.

arXiv comment22 pages; comments welcome

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Cited by in corpus (4)

• Stability of a Szegő-type asymptotics
• The Widom-Sobolev formula for discontinuous matrix-valued symbols
• Enhanced area law in the Widom-Sobolev formula for the free Dirac operator in arbitrary dimension
• An enhanced term in the Szegő-type asymptotics for the free massless Dirac operator