Regular Markov chains for which the transition matrix has large exponent
The exponent \(\exp(T)\) of a primitive \((n\times n)\) nonnegative matrix \(T\) is the smallest positive integer \(r\) for which \(T^r\) is positive. The authors investigate, using condition numbers, the stability of the stationary distributions of \((n\times n)\) primitive stochastic matrices \(P\) for which \(\exp(P)\geq [{(n-1)^2+ 1\over 2}]+ 2\). The work is a sequel to that of \textit{S. J. Kirkland} [Linear Algebra Appl. 253, 103-112 (1997; Zbl 0878.15015)].
scientific article; zbMATH DE number 1532992
scientific article