Non-negative Matrices and Markov Chains

By Eugene Seneta. 2008

2,224 citations recorded by the source corpus.

Subfields: Statistical and Nonlinear Physics

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Citations in the corpus

Stochastic Gradient Push for Distributed Deep Learning (2018, background): “Drawing inspiration from the theory of Markov chains (Seneta, 1981), the mixing matrices P (k) are designed to be column stochastic (each column must sum to 1).”
Aggregation methods in dynamical systems and applications in population and community dynamics (2008, background): “We refer the reader to [45] for details.”
New conditions for synchronization in dynamical communication networks (2011, methodology): “Then, B is called a scrambling matrix if λ(B) > 0 [22].”
Average Consensus in the Presence of Delays in Directed Graph Topologies (2014, background): “A special case of (asymptotic) consensus is the case of (asymptotic) average consensus, where the additional challenge is for the nodes to converge to the exact average of their initial values (see, for example, [2], [3]).”
Circular law theorem for random Markov matrices (2008, neutral): “If q = 0 then M has a complete skeleton, is aperiodic, and 1 is the sole eigenvalue of unit module [36].”
A non‐conservative Harris ergodic theorem (2019, methodology): “Finally, Hilbert metric and Birkhoff contraction yield another powerful method for analysis of semigroup, which has been well developed [17, 79, 87].”
Effective graph resistance (2011, background): “from [9], using the fact that λ = 1 is the unique maximum eigenvalue in absolute value of an irreducible stochastic matrix.”
Opinion Dynamics and the Evolution of Social Power in Influence Networks (2015, background): “The convex averaging model is related to the study of Markov chains [65] and is relevant in several”
Distributed Policy Evaluation Under Multiple Behavior Strategies (2013, background): “, there exists j > 0 such that all entries of C are strictly positive) [19], [46].”
A Necessary and Sufficient Condition for Consensus Over Random Networks (2008, background): “Although one may consider the difference to be an important one, that is not the case here because of the following theorem [2], [18]: Theorem 1: Given a matrix sequence {Wk}k=0 and their left products U (k,p) = Wk+p · · ·Wp+1, weak and strong ergodicity are equivalent.”
Liaisons dangereuses: Increasing connectivity, risk sharing, and systemic risk (2012, positive): “The graph has to be primitive (Seneta, 2006).”
Consensus-based distributed optimization: Practical issues and applications in large-scale machine learning (2012, methodology): “) Convergence properties of backward products of stochastic matrices are typically obtained by establishing weak ergodicity [27]; i.”
Distributed control of positive systems (2011, neutral): “It also appears in the study of Markov chains [21], where the states denote nonnegative probabilities and in compartment models [9] to model for example populations of species.”