随机矩阵乘积谱半径的大数定律

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics Pub Date : 2019-08-20 DOI:10.1353/AJM.2021.0025

Richard Aoun, Cagri Sert

引用次数: 10

摘要

证明了${\rm GL}_d(\Bbb{C})$上的i - id随机漫步的谱半径满足有限第二矩条件下的强大数定律和有限一矩条件下的弱大数定律。不假设不可约性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Law of large numbers for the spectral radius of random matrix products

abstract:We prove that the spectral radius of an i.i.d. random walk on ${\rm GL}_d(\Bbb{C})$ satisfies a strong law of large numbers under finite second moment assumption and a weak law of large numbers under finite first moment. No irreducibility assumption is supposed.

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来源期刊

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.