Stability of Asymptotics of Christoffel-Darboux Kernels

Jonathan Breuer; Yoram Last; Barry Simon

doi:10.1007/s00220-014-1913-4

Stability of Asymptotics of Christoffel-Darboux Kernels

Jonathan Breuer^*, Yoram Last, Barry Simon

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We study the stability of convergence of the Christoffel-Darboux kernel, associated with a compactly supported measure, to the sine kernel, under perturbations of the Jacobi coefficients of the measure. We prove stability under variations of the boundary conditions and stability in a weak sense under ℓ ¹ and random ℓ ² diagonal perturbations. We also show that convergence to the sine kernel at x implies that μ({x}) = 0.

Original language	English
Pages (from-to)	1155-1178
Number of pages	24
Journal	Communications in Mathematical Physics
Volume	330
Issue number	3
DOIs	https://doi.org/10.1007/s00220-014-1913-4
State	Published - Sep 2014

Bibliographical note

Funding Information:
J. Breuer, Y. Last: Supported in part by The Israel Science Foundation (Grant No. 1105/10).

Funding Information:
B. Simon: Supported in part by NSF Grant No. DMS-0968856.

Funding Information:
J. Breuer, Y. Last, B. Simon: Research supported in part by Grant No. 2010348 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.

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10.1007/s00220-014-1913-4

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abstract = "We study the stability of convergence of the Christoffel-Darboux kernel, associated with a compactly supported measure, to the sine kernel, under perturbations of the Jacobi coefficients of the measure. We prove stability under variations of the boundary conditions and stability in a weak sense under ℓ 1 and random ℓ 2 diagonal perturbations. We also show that convergence to the sine kernel at x implies that μ({x}) = 0.",

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N2 - We study the stability of convergence of the Christoffel-Darboux kernel, associated with a compactly supported measure, to the sine kernel, under perturbations of the Jacobi coefficients of the measure. We prove stability under variations of the boundary conditions and stability in a weak sense under ℓ 1 and random ℓ 2 diagonal perturbations. We also show that convergence to the sine kernel at x implies that μ({x}) = 0.

AB - We study the stability of convergence of the Christoffel-Darboux kernel, associated with a compactly supported measure, to the sine kernel, under perturbations of the Jacobi coefficients of the measure. We prove stability under variations of the boundary conditions and stability in a weak sense under ℓ 1 and random ℓ 2 diagonal perturbations. We also show that convergence to the sine kernel at x implies that μ({x}) = 0.

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Stability of Asymptotics of Christoffel-Darboux Kernels

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