期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1980
卷号：77
期号：7
页码：3749-3752
DOI：10.1073/pnas.77.7.3749
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Consider a sequence of N x N random nonnegative matrices in which each element depends on a vector u of parameters. The nth partial product is the random matrix formed by multiplying, from right to left, the first n of these random matrices in order. Under certain conditions, the elements of the nth partial product grow asymptotically exponentially as n increases, and the logarithms of the discrete long-run growth rates are convex functions of u. These conditions are met by some models in statistical mechanics and demography. Consequently, the Helmholtz free energy is concave and the population growth rate is convex in these models.
