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arXiv · 1610.10030

Traces of random operators associated with self-affine Delone sets and Shubin's formula

Scott Schmieding·Rodrigo Treviño
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Abstract

We study operators defined on a Hilbert space defined by a self-affine Delone set $\Lambda$ and show that the usual trace of a restriction of the operator to finite-dimensional subspaces satisfies a certain $\limsup$ law controlled by traces on a certain subalgebra. The asymptotic traces are defined through asymptotic cycles, or $\mathbb{R}^d$-invariant distributions of a dynamical system defined by $\Lambda$. We use this to refine Shubin's trace formula for self-adjoint operators and show that the errors of convergence in Shubin's formula are given by these traces.

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Scott Schmieding, Rodrigo Treviño. 2016-10-31. Traces of random operators associated with self-affine Delone sets and Shubin's formula. https://doi.org/10.1007/s00023-018-0700-8

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