Geodesic
Difference Operators and Determinantal Point Processes
Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 4, pp. 83-97

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper deals with a family $\{P\}$ of determinantal point processes arising in representation theory and random matrix theory. The processes $P$ live on a one-dimensional lattice and have a number of special properties. One of them is that the correlation kernel $K(x,y)$ of each of the processes is a projection kernel: it determines a projection $K$ in the Hilbert $\ell^2$ space on the lattice. Moreover, the projection $K$ can be realized as the spectral projection onto the positive part of the spectrum of a self-adjoint difference second-order operator $D$. The aim of the paper is to show that the difference operators $D$ can be efficiently used in the study of limit transitions within the family $\{P\}$.
Keywords: point process, determinantal process, Plancherel measure, z-measure
Mots-clés : orthogonal polynomial ensemble, Meixner polynomial, Krawtchouk polynomial. 
@article{FAA_2008_42_4_a6,
     author = {G. I. Olshanskii},
     title = {Difference {Operators} and {Determinantal} {Point} {Processes}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {83--97},
     publisher = {mathdoc},
     volume = {42},
     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2008_42_4_a6/}
}
TY  - JOUR
AU  - G. I. Olshanskii
TI  - Difference Operators and Determinantal Point Processes
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2008
SP  - 83
EP  - 97
VL  - 42
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2008_42_4_a6/
LA  - ru
ID  - FAA_2008_42_4_a6
ER  - 
%0 Journal Article
%A G. I. Olshanskii
%T Difference Operators and Determinantal Point Processes
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2008
%P 83-97
%V 42
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2008_42_4_a6/
%G ru
%F FAA_2008_42_4_a6
G. I. Olshanskii. Difference Operators and Determinantal Point Processes. Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 4, pp. 83-97. http://geodesic.mathdoc.fr/item/FAA_2008_42_4_a6/