A CLASS OF MARKOV CHAINS WITH NO SPECTRAL GAP

作者：Kovchegov Yevgeniy^*; Michalowski Nicholas

来源：Proceedings of the American Mathematical Society, 2013, 141(12): 4317-4326.

In this paper we extend the results of the research started by the first author in which Karlin-McGregor diagonalization of certain reversible Markov chains over countably infinite general state spaces by orthogonal polynomials was used to estimate the rate of convergence to a stationary distribution. %26lt;br%26gt;We use a method of Koornwinder to generate a large and interesting family of random walks which exhibits a lack of spectral gap, and a polynomial rate of convergence to the stationary distribution. For the Chebyshev type subfamily of Markov chains, we use asymptotic techniques to obtain an upper bound of order O(log t/root t) and a lower bound of order O(1/root t) on the distance to the stationary distribution regardless of the initial state. Due to the lack of a spectral gap, these results lie outside the scope of geometric ergodicity theory.

• 出版日期2013-12