Hi,

 

Given a positive integer N, and a real number \lambda such that 0 < \lambda
< 1,  I would like to generate an N by N stochastic matrix (a matrix with
all the rows summing to 1), such that it has the second largest eigenvalue
equal to \lambda (Note: the dominant eigenvalue of a stochastic matrix is
1).  

 

I don't care what the other eigenvalues are.  The second eigenvalue is
important in that it governs the rate at which the random process given by
the stochastic matrix converges to its stationary distribution.

 

Does anyone know of an algorithm to do this?

 

Thanks for any help,

Ravi.

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Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology 

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan@jhmi.edu

Webpage:
<http://www.jhsph.edu/agingandhealth/People/Faculty_personal_pages/Varadhan.
html>
http://www.jhsph.edu/agingandhealth/People/Faculty_personal_pages/Varadhan.h
tml

 

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