Difference operators and determinantal point processes

Understand

We consider a family {P} of determinantal point processes arising in representation theory and random matrix theory.

• The processes live on the one-dimensional lattice and their correlation kernels correspond to projection operators in the l^2 Hilbert space on the lattice.
• Moreover, these projections are spectral projections associated to certain selfadjoint second order difference operators on the lattice.
• The aim of the note is to demonstrate that the difference operators in question can be efficiently employed in the study of limit transitions inside the family {P}.