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. ---------------------------------------------------------------------------- ------- 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: rvarad...@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 ---------------------------------------------------------------------------- -------- [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
