2016/05/04 by Bufetov, Alexander I.
Mathematics · #Random Matrices and Applications #Mathematical functions and polynomials #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1605.01400
For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the configuration in the complement of a compact interval, are orthogonal polynomial ensembles with explicitly found weights. Examples include the sine-process and the process with the Bessel kernel. The argument uses the quasi-invariance, established in [1], of our point processes under the group of piecewise isometries of the real line.