naa a22 4500 510810411 CHVBK 20180411083440.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s12220-011-9238-4 doi (NATIONALLICENCE)springer-10.1007/s12220-011-9238-4 Ameur Yacin Department of Mathematics, Luleå University of Technology, 971 87, Luleå, Sweden aut Near-Boundary Asymptotics for Correlation Kernels [Elektronische Daten] [Yacin Ameur] We discuss asymptotic formulas for the correlation kernel corresponding to a (more or less) general potential Q in the plane. If K n is such a kernel, there is a known asymptotic formula K n (z,z)=nΔQ(z)+B 1(z)+n −1 B 2(z)+⋯ valid for z in the interior of a certain compact set known as the "droplet” corresponding to Q (on which ΔQ>0). On the other hand, if z is in the exterior of the droplet, K n (z,z) converges to zero exponentially inn. Results of this type are useful in random matrix theory and conformal field theory; they have recently been used to prove the Gaussian field convergence in the interior of the droplet for fluctuations of eigenvalues of random normal matrices. To be able to extend such results beyond the interior, it becomes necessary to have a certain uniformity of estimates as z approaches the boundary either from the interior or from the exterior. Such estimates have to our knowledge hitherto not been known on a rigorous level. This note intends to fill this gap. We will consider applications in later publications. Our treatment of the (interior) asymptotics relies in an essential way on previous work due to Berman, Berndtsson, and Sjöstrand (Ark. Mat. 46, 2008), and Berman (Indiana Univ. Math. J. 58, 2009). We hope that this note can to some extent be regarded as a contribution to that work. Mathematica Josephina, Inc., 2011 Correlation kernel nationallicence Asymptotic expansion nationallicence Random normal matrix theory nationallicence Journal of Geometric Analysis Springer-Verlag 23/1(2013-01-01), 73-95 1050-6926 23:1<73 2013 23 12220 https://doi.org/10.1007/s12220-011-9238-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9238-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ameur Yacin Department of Mathematics, Luleå University of Technology, 971 87, Luleå, Sweden aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer-Verlag 23/1(2013-01-01), 73-95 1050-6926 23:1<73 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer