Determinantal Correlations for Classical Projection Processes

Abstract

Recent applications in queuing theory and statistical mechanics have isolated the process formed by the eigenvalues of successive minors of the GUE. Analogous eigenvalue processes, formed in general from the eigenvalues of nested sequences of matrices resulting from random corank 1 projections of classical random matrix ensembles, are identified for the LUE and JUE. The correlations for all these processes can be computed in a unified way. The resulting expressions can then be analyzed in various scaling limits. At the soft edge, with the rank of the minors differing by an amount proportional to $N^{2/3}$, the scaled correlations coincide with those known from the soft edge scaling of the Dyson Brownian motion model.

26 pages

References in corpus (4)

• Fluctuation properties of the TASEP with periodic initial configuration
• Transition between Airy_1 and Airy_2 processes and TASEP fluctuations
• Airy kernel with two sets of parameters in directed percolation and random matrix theory
• The bead model and limit behaviors of dimer models

Cited by in corpus (7)

• Airy kernel with two sets of parameters in directed percolation and random matrix theory
• On the largest-eigenvalue process for generalized Wishart random matrices
• Interlaced particle systems and tilings of the Aztec diamond
• The Dyson Brownian minor process
• A Finitization of the Bead Process
• Interlaced processes on the circle
• Limit theorems for linear eigenvalue statistics of overlapping matrices