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Stability of Asymptotics of Christoffel–Darboux Kernels

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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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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University, 91904, Jerusalem, Israel

    Jonathan Breuer & Yoram Last

  2. Mathematics 253-37, California Institute of Technology, Pasadena, CA, 91125, USA

    Barry Simon

Authors
  1. Jonathan Breuer
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  2. Yoram Last
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  3. Barry Simon
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Corresponding author

Correspondence to Jonathan Breuer.

Additional information

Communicated by L. Erdos

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

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

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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Breuer, J., Last, Y. & Simon, B. Stability of Asymptotics of Christoffel–Darboux Kernels. Commun. Math. Phys. 330, 1155–1178 (2014). https://doi.org/10.1007/s00220-014-1913-4

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  • DOI: https://doi.org/10.1007/s00220-014-1913-4

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