Lyapunov exponents for truncated unitary and Ginibre matrices

被引：2

作者：

Ahn, Andrew ^{[1
]}

Van Peski, Roger ^{[2
]}

机构：

[1] Cornell Univ, Dept Math, Ithaca, NY 14850 USA

[2] MIT, Dept Math, Cambridge, MA USA

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2023年 / 59卷 / 02期

关键词：

Random matrix products; Lyapunov exponents; Picket fence statistics; PRODUCTS;

D O I：

10.1214/22-AIHP1268

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this note, we show that the Lyapunov exponents of mixed products of random truncated Haar unitary and complex Ginibre matrices are asymptotically given by equally spaced 'picket-fence' statistics. We discuss how these statistics should originate from the connection between random matrix products and multiplicative Brownian motion on GLn(C), analogous to the connection between discrete random walks and ordinary Brownian motion. Our methods are based on contour integral formulas for products of classical matrix ensembles from integrable probability.

引用

页码：1029 / 1039

页数：11

共 30 条

[1]

Aggarwal A., 2021, ARXIV

[2]

Aggarwal A, 2023, Arxiv, DOI arXiv:2108.12874

[3]

Aggarwal A, 2023, Arxiv, DOI arXiv:1907.09991

[4]

Ahn A, 2022, Arxiv, DOI arXiv:2201.11809

[5]

Ahn A, 2020, Arxiv, DOI arXiv:1910.00743

[6]

Akemann G, 2020, Arxiv, DOI arXiv:2008.11470

[7] From integrable to chaotic systems: Universal local statistics of Lyapunov exponents [J].

Akemann, Gernot ;

Burda, Zdzislaw ;

Kieburg, Mario .

EPL, 2019, 126 (04)

[8]

[Anonymous], 1993, Springer series in Solid-State Sciences, DOI DOI 10.1007/978-3-642-84942-8

[9] LIMIT THEOREMS FOR NON-COMMUTATIVE OPERATIONS .1. [J].

BELLMAN, R .

DUKE MATHEMATICAL JOURNAL, 1954, 21 (03) :491-500

[10] Product Matrix Processes as Limits of Random Plane Partitions [J].

Borodin, Alexei ;

Gorin, Vadim ;

Strahov, Eugene .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2020, 2020 (20) :6713-6768

← 1 2 3 →