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 -