Painlevé formulas of the limiting distributions for nonnull complex sample covariance matrices
By Jinho Baik. 2005
66 citations recorded by the source corpus.
In a recent study of large non-null sample covariance matrices, a new sequence of functions gener- alizing the GUE Tracy-Widom distribution of random matrix theory was obtained. This paper derives Painleve formulas of these functions and use them to prove that they are indeed distribution functions. Applications of these new distribution functions to last passage percolation, queues in tandem and to- tally asymmetric simple exclusion process are also discussed. As a part of the proof, a representation of orthogonal polynomials on the unit circle in terms of an operator on a discrete set is presented.
Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/3e5958bd0b06364b9b572cf38d7e5ac139c9e5d6
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
- Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension (2012, methodology): “[7]) and we use the most convenient for our purposes.”
- Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices (2004, methodology): “The fact that Fk(x) → 0 as x → −∞ is obtained in [4] using the Painlevé formula.”
- The Distributions of Random Matrix Theory and their Applications (2009, background): “If π1 = wc the limiting distribution is a generalization of F2 expressible in terms of the same Painlevé II function q [1].”