Equivalence of Palm measures for determinantal point processes associated with Hilbert spaces of holomorphic functions

A. Bufetov; Qiu Y.

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Equivalence of Palm measures for determinantal point processes associated with Hilbert spaces of holomorphic functions

Comptes Rendus Mathematique. 2015. Vol. 353. No. 6. P. 551–555.

Bufetov A., Qiu Y.

We obtain explicit formulae, in the form of regularized multiplicative functionals related to certain Blaschke products, of the Radon-Nikodym derivatives between reduced Palm measures of all orders for determinantal point processes associated with a large class of weighted Bergman spaces on the disk. Our method also applies to determinantal point processes associated with weighted Fock spaces. © 2015 Académie des sciences.

Language: English

Keywords: Hilbert spaces

Orthorecursive expansion of unity

Kalmynin A. B., Kosenko P., / Series math "arxiv.org". 2019. No. 1901.04004.

We study the properties of a sequence c_n defined by the recursive relation c_0/(n+1)+c_1/(n+2)+…+c_n/(2n+1)=0 for n>1 and c_0=1. This sequence also has an alternative definition in terms of certain norm minimization in the space L^2([0,1]). We prove estimates on growth order of c_n and the sequence of its partial sums, infinite series identities, connecting c_n with harmonic numbers H_n and also formulate some conjectures based on numerical ...

Added: July 17, 2019

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Cadre B., Paris Quentin, TEST 2012 Vol. 21 No. 2 P. 301–316

Based on n randomly drawn vectors in a Hilbert space, we study the k-means clustering scheme. Here, clustering is performed by computing the Voronoi partition associated with centers that minimize an empirical criterion, called distorsion. The performance of the method is evaluated by comparing the theoretical distorsion of empirical optimal centers to the theoretical optimal distorsion. Our first ...

Added: December 20, 2014