4 research outputs found
Sharp entrywise perturbation bounds for Markov chains
For many Markov chains of practical interest, the invariant distribution is
extremely sensitive to perturbations of some entries of the transition matrix,
but insensitive to others; we give an example of such a chain, motivated by a
problem in computational statistical physics. We have derived perturbation
bounds on the relative error of the invariant distribution that reveal these
variations in sensitivity.
Our bounds are sharp, we do not impose any structural assumptions on the
transition matrix or on the perturbation, and computing the bounds has the same
complexity as computing the invariant distribution or computing other bounds in
the literature. Moreover, our bounds have a simple interpretation in terms of
hitting times, which can be used to draw intuitive but rigorous conclusions
about the sensitivity of a chain to various types of perturbations
Nonlocal PageRank
In this work we introduce and study a nonlocal version of the PageRank. In
our approach, the random walker explores the graph using longer excursions than
just moving between neighboring nodes. As a result, the corresponding ranking
of the nodes, which takes into account a \textit{long-range interaction}
between them, does not exhibit concentration phenomena typical of spectral
rankings which take into account just local interactions. We show that the
predictive value of the rankings obtained using our proposals is considerably
improved on different real world problems
Strong Truncation Approximation in Tandem Queues with Blocking
Markov models are frequently used for performance modeling. However most models do not have closed form solutions, and numerical solutions are often not feasible due to the large or even infinite state space of models of practical interest. For that, the state-space truncation is often demanded for computation of this kind of models. In this paper, we use the strong stability approach to establish analytic error bounds for the truncation of a tandem queue with blocking. Numerical examples are carried out to illustrate the quality of the obtained error bounds