Products of indecomposable, aperiodic, stochastic matrices

By J. Wolfowitz. 1963

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination (2012, background): “A ro w stochastic matrixP ∈ R is called indecomposable and aperiodic if limk→∞ P k = 1y for somey ∈ R [25].”
Defending non-Bayesian learning against adversarial attacks (2016, positive): “]···A[r] for 1 ≤r≤t+ 1. By convention, Φ(t,t) = A[t] and Φ(t,t+ 1) = I. Note that Φ(t,r) is a backward product. Using prior work on coeﬃcients of ergodicity [9], under Assumption 1, it has been shown [28,19] that lim t≥r, t→∞ Φ(t,r) = 1π(r), (3) where π(r) ∈Rn−φ is a row stochastic vector, and 1 is ”
Coordination of groups of mobile autonomous agents using nearest neighbor rules (2002, methodology): “In [4] and [5], Toner and Tu construct a continuous ”hydrodynamic" model of the group of agents, while other authors such as Mikhailov and Zanette [6] consider the behavior of populations of self propelled particles with long range interactions.”
Sampled-data discrete-time coordination algorithms for double-integrator dynamics under dynamic directed interaction (2010, unknown): “1 column vector (Wolfowitz 1963).”
Constrained Consensus and Optimization in Multi-Agent Networks (2008, background): “The convergence properties of these matrices as have been extensively studied and well-established (see [1], [5], [26]).”
Average Consensus in the Presence of Delays in Directed Graph Topologies (2014, methodology): “Theorem 1: [18] Let be a collection of column stochastic matrices of order such that any word in the ’s is stochastic, indecomposable, and aperiodic (SIA).”
Consensus and Cooperation in Networked Multi-Agent Systems (2007, background): “The problem of convergence of infinite product of stochastic matrices has a long history and has been studied by several mathematicians including Wolfowitz [ 100 ].”
A survey of consensus problems in multi-agent coordination (2005, background): “The classical result in [8] demonstrates the property of the”
Asynchronous Consensus in Continuous-Time Multi-Agent Systems With Switching Topology and Time-Varying Delays (2006, background): “Lemma 4 ([33], Lemma 2) For any stochastic matrices A1, A2, · · · , Ak, k > 0, δ(A1A2 · · ·Ak) ≤ k ∏”
Information consensus in multivehicle cooperative control (2007, background): “chastic matrix A is indecomposable and aperiodic (SIA) if limk→∞ Ak = 1νT , where ν is a column vector [29].”
Consensus protocols for discrete-time multi-agent systems with time-varying delays (2008, background): “By Lemma 2 of Wolfowitz (1963) δ( ∏l i=1 Ai) ≤ ∏j−1 p=0 λ( ∏(p+1)k i=1+pk Ai) ≤ λ j m.”
Technical communique: Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies (2009, unknown): “Lemma 1 ( Wolfowitz, 1963).”
Cooperative Control of Dynamical Systems With Application to Autonomous Vehicles (2009, background): “It was first reported in [ 44 ] and then restated in [23] and [48], and its proof is based upon the simple yet powerful inequality of”