Eigenvalues of GUE Minors

By K. Johansson, Eric Nordenstam. 2006

147 citations recorded by the source corpus.

Consider an infinite random matrix $H=(h_{ij})_{0 < i,j}$ picked from the Gaussian Unitary Ensemble (GUE). Denote its main minors by $H_i=(h_{rs})_{1\leq r,s\leq i}$ and let the $j$:th largest eigenvalue of $H_i$ be $\mu^i_j$. We show that the configuration of all these eigenvalues $(i,\mu_j^i)$ form a determinantal point process on $\mathbb{N}\times\mathbb{R}$. Furthermore we show that this process can be obtained as the scaling limit in random tilings of the Aztec diamond close to the boundary. We also discuss the corresponding limit for random lozenge tilings of a hexagon. An Erratum to this paper has been published in Electronic Journal of Probability, Volume 12 (2007), paper number 37 .

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d78bc83e05664446d3bc421ec7e0efe80e83f2c1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Stochastic six-vertex model (2014, background): “ of random domino tilings of the Aztec diamond, see [EKLP], [Ku], [FS1] for the details. Uniformly random tilings of the Aztec diamond are known to posses random matrix asymptotic behavior, see [J3], [JN]. However, we do not know any direct relation of our measures P(b 1;b 2) with free fermion point”
Nonintersecting paths and the Hahn orthogonal polynomial ensemble (2008, methodology): “Cohn–Larsen-Propp [CLP], Johansson [J], Johansson–Nordenstam [ JN ]).”
On adding a list of numbers (and other one-dependent determinantal processes) (2009, background): “We first describe some results for the stationary case.”