Additive functionals of the determinantal point process with confluent hypergeometric kernel converge to Gaussian with a Kolmogorov-Smirnov distance estimate as R tends to infinity.
Correlations for symplectic and orthogonal Schur measures
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abstract
We show, using either Fock space techniques or Macdonald difference operators, that certain symplectic and orthogonal analogues of Okounkov's Schur measure are determinantal with kernels given by explicit double contour integrals. We give two applications: one equates certain Toeplitz+Hankel determinants of random matrix theory with appropriate Fredholm determinants and computes Szeg\H{o} asymptotics for the former; another finds that the simplest examples of said measures exhibit discrete sine kernel asymptotics in the bulk and Airy 2 to 1 kernel---along with a certain dual---asymptotics at the edge. We believe the edge behavior to be universal.
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Central limit theorem for the determinantal point process with the confluent hypergeometric kernel
Additive functionals of the determinantal point process with confluent hypergeometric kernel converge to Gaussian with a Kolmogorov-Smirnov distance estimate as R tends to infinity.