Perturbation theory and finite Markov chains

By P. Schweitzer. 1968

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Citations in the corpus

Deep Generative Stochastic Networks Trainable by Backprop (2013, methodology): “Adapted from (Schweitzer, 1968) Let K be the transition matrix of a ﬁnite state, irreducible, homogeneous Markov chain.”
Comparison of perturbation bounds for the stationary distribution of a Markov chain (2001, unknown): “…all k = 1, 2, · · · , n,(3.5) where A(j) is the principal submatrix of A obtained by deleting the j-th row and column from A. Kirkland, Neumann, and Shader [9] improved the perturbation bound in (3.5) by a factor of 2: ‖π − π̃‖∞ minj ‖A−1(j)‖ 2 ‖E‖∞, giving the condition number κ7 ≡ minj…”
The Role of Kemeny's Constant in Properties of Markov Chains (2012, methodology): “Using the above characterisation, Zhou and Trinajstic, (2009), found upper and lower bounds for Kf (G) in terms of the eigenvalues of the normalised Laplacian L = DLD .”
Spread of (mis)information in social networks (2009, methodology): “The theorem is based on a result due to Schweitzer [33] (see also Haviv and Van Der Heyden [25]).”
Graph fibrations, graph isomorphism, and PageRank (2006, background): “These generalisations naturally lead to recast PageRank as a special case of a perturbed Markov chain [19, 29] that we call Markov chain with restart.”
Opinion Dynamics and Learning in Social Networks (2011, unknown): “in particular, [57, 83]).”
Markov chain sensitivity measured by mean first passage times (2000, background): “Markov chains, stationary distribution, mean first passage times, stochastic matrix, sensitivity analysis, perturbation theory, stability of a Markov chain, condition numbers AMS subject classifications.”
Gene perturbation and intervention in probabilistic Boolean networks (2002, methodology): “Boolean networks and PBNs also exhibit this behavior, the former with fixed point and limit cycle attractors (Kauffman, 1993), the latter with absorbing states and irreducible sets of states (Shmulevich et al., 2002).”