Universality limits at the soft edge of the spectrum via classical complex analysis

Eli Levin; Doron S. Lubinsky

doi:10.1093/imrn/rnq185

Universality limits at the soft edge of the spectrum via classical complex analysis

Eli Levin, Doron S. Lubinsky

Mathematics discipline

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

Abstract

We show that universality at the soft edge of the spectrum is equivalent to universality "along the diagonal," that is ratio asymptotics for Christoffel functions. The context is that of varying measures and limits involving the Airy kernel. In particular, we consider measures of the form, where W_n²ⁿ(x) dx, where {W_n} are a suitable sequence of weights. They do not need to be analytic, but instead should satisfy some hypotheses on the associated equilibrium measures.

Original language	English
Pages (from-to)	3006-3070
Number of pages	65
Journal	International Mathematics Research Notices
Volume	2011
Issue number	13
DOIs	https://doi.org/10.1093/imrn/rnq185
State	Published - 2011

Bibliographical note

Funding Information:
tional Science Foundation grant 2008399.

Funding Information:
The work was supported by National Science Foundation grant DMS1001182 and US-Israel Bina-

Access to Document

10.1093/imrn/rnq185

Cite this

@article{b1eba7b3aed348e2a4f28e141a12c979,

title = "Universality limits at the soft edge of the spectrum via classical complex analysis",

abstract = "We show that universality at the soft edge of the spectrum is equivalent to universality {"}along the diagonal,{"} that is ratio asymptotics for Christoffel functions. The context is that of varying measures and limits involving the Airy kernel. In particular, we consider measures of the form, where Wn2n(x) dx, where {Wn} are a suitable sequence of weights. They do not need to be analytic, but instead should satisfy some hypotheses on the associated equilibrium measures.",

author = "Eli Levin and Lubinsky, {Doron S.}",

note = "Funding Information: tional Science Foundation grant 2008399. Funding Information: The work was supported by National Science Foundation grant DMS1001182 and US-Israel Bina-",

year = "2011",

doi = "10.1093/imrn/rnq185",

language = "אנגלית",

volume = "2011",

pages = "3006--3070",

journal = "International Mathematics Research Notices",

issn = "1073-7928",

publisher = "Oxford University Press",

number = "13",

}

TY - JOUR

T1 - Universality limits at the soft edge of the spectrum via classical complex analysis

AU - Levin, Eli

AU - Lubinsky, Doron S.

N1 - Funding Information: tional Science Foundation grant 2008399. Funding Information: The work was supported by National Science Foundation grant DMS1001182 and US-Israel Bina-

PY - 2011

Y1 - 2011

N2 - We show that universality at the soft edge of the spectrum is equivalent to universality "along the diagonal," that is ratio asymptotics for Christoffel functions. The context is that of varying measures and limits involving the Airy kernel. In particular, we consider measures of the form, where Wn2n(x) dx, where {Wn} are a suitable sequence of weights. They do not need to be analytic, but instead should satisfy some hypotheses on the associated equilibrium measures.

AB - We show that universality at the soft edge of the spectrum is equivalent to universality "along the diagonal," that is ratio asymptotics for Christoffel functions. The context is that of varying measures and limits involving the Airy kernel. In particular, we consider measures of the form, where Wn2n(x) dx, where {Wn} are a suitable sequence of weights. They do not need to be analytic, but instead should satisfy some hypotheses on the associated equilibrium measures.

UR - http://www.scopus.com/inward/record.url?scp=79960151177&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnq185

DO - 10.1093/imrn/rnq185

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:79960151177

SN - 1073-7928

VL - 2011

SP - 3006

EP - 3070

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 13

ER -

Universality limits at the soft edge of the spectrum via classical complex analysis

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this