Universality limits in the bulk for varying measures

Levin, Eli; Lubinsky, D. S.

doi:10.1016/j.aim.2008.06.010

Cited by 68 publications

(80 citation statements)

References 38 publications

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“…There is a large literature on this. Some recent references are [3], [14], [16], [17], [18], [19], [20], [27], [31].…”

Section: Results 1 Let Be a …Nite Positive Borel Measure With Compactmentioning

confidence: 99%

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Universality Limits at the Hard Edge of the Spectrum for Measures with Compact Support

Lubinsky

2010

International Mathematics Research Notices

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“…There is a large literature on this. Some recent references are [3], [14], [16], [17], [18], [19], [20], [27], [31].…”

Section: Results 1 Let Be a …Nite Positive Borel Measure With Compactmentioning

confidence: 99%

“…It is the analogue for the hard edge, of a method that has worked well in the bulk, for measures on compact sets [20] and for exponential and varying weights [17]. It should in principle allow an extension of Theorem 1.1 to measures with general compact support.…”

Section: N=0mentioning

confidence: 99%

Universality Limits at the Hard Edge of the Spectrum for Measures with Compact Support

Lubinsky

2010

International Mathematics Research Notices

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“…As noted above, for regular measures, Totik and Findley assumed less on w. They assumed that log w is integrable in a neighborhood of , rather than w being bounded above and below by positive constants there. The methods of this paper may also be applied to varying weights [14].…”

Section: Introduction and Resultsmentioning

confidence: 99%

Universality limits in the bulk for arbitrary measures on compact sets

Lubinsky

2008

J Anal Math

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Abstract. We present a new method for establishing universality limits in the bulk, based on the theory of entire functions of exponential type. Let be a measure on a compact subset of the real line. Assume that is absolutely continuous in a neighborhood of some point x in the support, and that 0 is bounded above and below near x, which is assumed to be a Lebesgue point of 0 . Then universality holds at x i¤ it holds "along the diagonal", that is lim n!1 Kn x + a n ; x + a n Kn (x; x) = 1;for all real a. The method does not require regularity of the measure as did earlier methods. Moreover, the assumption on the diagonal is certainly satis…ed in the case of regular measures, so that we obtain another proof of some recent results of Simon and Totik.

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“…The equilibrium density ρ has no zeros in (−θ, θ) and 8) and the function u (λ) of (1.5) attains its minimum if and only if λ belongs to σ.…”

Section: Introductionmentioning

confidence: 99%

“…The complete asymptotic expansion of the Jacobi matrix coefficients in the case of real analytic V and one or two interval equilibrium density ρ was constructed in [1]. These results were used to prove universality of local bulk and edge regimes of the hermitian matrix models with the potential V (see also [14], [13], [8]). The case of OPUC, with varying weight till now is not understood so well as the case of classical OP.…”

Section: Introductionmentioning

confidence: 99%