A Note on Perturbations of Stochastic Matrices

✍ Scribed by B. Huppert; W. Willems

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 104 KB
• Volume: 234
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2000.8544

✦ Synopsis

helmut wielandt zum 90. geburtstag Let A and B be stochastic matrices of the same type n n . It is natural to consider perturbations A t of A of the form

Now, the following two questions come up immediately.

(1) When does lim k→∞ A t k exist?

(2) How does lim k→∞ A t k behave for small t?

As the existence of lim k→∞ A t k depends only on the eigenvalues of A t , which are continuously dependent on t, question (1) allows a positive answer (see Section 1). The answer to question (2) is less simple. This