Aldous’ spectral gap conjecture asserts that on any graph the random walk process and the random transposition (or interchange) process have the same spectral gap. We prove the conjecture using a recursive strategy. The approach is a natural extension of the method already used to prove the validity of the conjecture on trees. The novelty is an idea based on electric network reduction which red...

abstract agricultural scientists have developed considerable interest in modeling and generation of rainfall as new ways of analyzing rainfall data and assessing its impact on agriculture. a combination of markov chain and gamma distribution function is recognized as a simple approach and is demonstrated to be effective in generating daily rainfall data for many environments. thus the availabil...

Suppose that A is an irreducible stochastic matrix of order n, and denote its eigenvalues by 1, λ2, . . . , λn. The Kemeny constant, K(A) for the Markov chain associated with A is defined as K(A) = ∑n j=2 1 1−λj , and can be interpreted as the mean first passage from an unknown initial state to an unknown destination state in the Markov chain. Let w denote the stationary distribution vector for...

Grassman, Taksar, and Heyman have proposed an algorithm for computing the stationary vector of a Markov chain. Analysis by O'Cinneide confirmed the results of numerical experiments, proving that the GTH algorithm computes an approximation to the stationary vector with low relative error in each component. In this work, we develop a block form of the GTH algorithm, more efficient on high-perform...

Suppose that A is an irreducible stochastic matrix of order n, and denote its eigenvalues by 1, λ2, . . . , λn. The Kemeny constant, K(A) for the Markov chain associated with A is defined as K(A) = ∑n j=2 1 1−λj , and can be interpreted as the mean first passage from an unknown initial state to an unknown destination state in the Markov chain. Let w denote the stationary distribution vector for...

By deriving a new set of tight perturbation bounds, it is shown that all stationary probabilities of a finite irreducible Markov chain react essentially in the same way to perturbations in the transition probabilities. In particular, if at least one stationary probability is insensitive in a relative sense, then all stationary probabilities must be insensitive in an absolute sense. New measures...

In this paper, it is shown that nearly completely decomposable (NCD) Markov chains are quasi{lumpable. The state space partition is the natural one, and the technique may be used to compute lower and upper bounds on the stationary probability of each NCD block. In doing so, a lower bounding nonnegative coupling matrix is employed. The nature of the stationary probability bounds is closely relat...

We study asymptotic behavior of a Markov semigroup on a von-Neumann algebra by exploring a maximal von-Neumann subalgebra where the Markov semigroup is an automorphism. This enables us to prove that strong mixing is equivalent to ergodic property for continuous time Markov semigroup on a type-I von-Neumann algebra with center completely atomic. For discrete time dynamics we prove that an aperio...

Given access to a single long trajectory generated by an unknown irreducible Markov chain M, we simulate $$\alpha $$ -lazy version of M which is ergodic. This enables us generalize recent results on estimation and identity testing, that were stated for ergodic chains, in way allows fully empirical inference. In particular, our approach shows the pseudo spectral gap introduced Paulin (Electron J...