2006/10/31 by Alexei Borodin, Grigori Olshanski · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Random Matrices and Applications #math-ph #math.MP #math.PR #msc:33C45 #msc:60C05 #msc:60G55
paper · pdf · doi:10.1016/j.jalgebra.2006.10.039
published as J. Algebra 313 (2007), no. 1, 40-60. · AMS TeX, 19 pages. Version 2: minor typos fixed
openalex publication_date 2007/01/25 · arxiv created 2007/02/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
We present a solution to a problem suggested by Philippe Biane: We prove that a certain Plancherel-type probability distribution on partitions converges, as partitions get large, to a new determinantal random point process on the set 0,1,2,... of nonnegative integers. This can be viewed as an edge limit ransition. The limit process is determined by a correlation kernel on 0,1,2,... which is expressed through the Hermite polynomials, we call it the discrete Hermite kernel. The proof is based on a simple argument which derives convergence of correlation kernels from convergence of unbounded self-adjoint difference operators. Our approach can also be applied to a number of other probabilistic models. As an example, we discuss a bulk limit for one more Plancherel-type model of random partitions.