BULK ASYMPTOTICS FOR POLYANALYTIC CORRELATION KERNELS

Abstract. For a weight function Q: C → R and a positive scaling parameter m, we study reproducing kernels Kq,mQ,nof the polynomial spaces A2q,mQ,n: = spanC{z̄rzj | 0 ≤ r ≤ q − 1, 0 ≤ j ≤ n − 1} equipped with the inner product from the space L2 e−mQ(z)dA(z). Here dA denotes a suitably normalized area measure on C. For a point z0 belonging to the interior of certain compact set S and satisfying ∆Q(z0)> 0, we define the rescaled coordinates z = z0 + ξ√ m∆Q(z0), w = z0 + λ√ m∆Q(z0) The following universality result is proved in the case q = 2: 1 m∆Q(z0) |Kq,mQ,n(z, w)|e