Shape Fluctuations and Random Matrices

Kurt Johansson

doi:10.1007/s002200050027

Shape Fluctuations and Random Matrices

组合数学 2009-10-31 v2 概率论

作者: Kurt Johansson

在 arXiv 上查看 ↗ PDF ↗ DOI ↗

摘要

We study a certain random groeth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble.

关键词

fluctuation theory random matrix theory gaussian random fields

引用

@article{arxiv.math/9903134,
  title  = {Shape Fluctuations and Random Matrices},
  author = {Kurt Johansson},
  journal= {arXiv preprint arXiv:math/9903134},
  year   = {2009}
}

备注

Revised version. 51 pages

相关论文

查看更多相关论文 →

信息论 · 计算机科学

Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy-Widom distribution

Marco Chiani

2014-10-21

统计力学 · 物理学

A simple derivation of the Tracy-Widom distribution of the maximal eigenvalue of a Gaussian unitary random matrix