TY - JOUR

T1 - Universality limits for exponential weights

AU - Levin, Eli

AU - Lubinsky, Doron S.

PY - 2009/4

Y1 - 2009/4

N2 - We establish universality in the bulk for fixed exponential weights on the whole real line. Our methods involve first-order asymptotics for orthogonal polynomials and localization techniques. In particular, we allow exponential weights such as | x | 2β g 2(x)exp∈(-2Q(x)), where β>-1/2, Q is convex and Q ″ satisfies some regularity conditions, while g is positive, and has a uniformly continuous and slowly growing or decaying logarithm.

AB - We establish universality in the bulk for fixed exponential weights on the whole real line. Our methods involve first-order asymptotics for orthogonal polynomials and localization techniques. In particular, we allow exponential weights such as | x | 2β g 2(x)exp∈(-2Q(x)), where β>-1/2, Q is convex and Q ″ satisfies some regularity conditions, while g is positive, and has a uniformly continuous and slowly growing or decaying logarithm.

KW - Exponential weights

KW - Orthogonal polynomials

KW - Universality limits

UR - http://www.scopus.com/inward/record.url?scp=60349109189&partnerID=8YFLogxK

U2 - 10.1007/s00365-008-9020-4

DO - 10.1007/s00365-008-9020-4

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AN - SCOPUS:60349109189

SN - 0176-4276

VL - 29

SP - 247

EP - 275

JO - Constructive Approximation

JF - Constructive Approximation

IS - 2

ER -