Analytically solvable processes on networks

Daniel Smilkov; Ljupco Kocarev

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Analytically solvable processes on networks

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arxiv 1103.2252 v2 pith:O5DQP673 submitted 2011-03-11 physics.soc-ph cond-mat.stat-mechcs.SI

Analytically solvable processes on networks

Daniel Smilkov , Ljupco Kocarev This is my paper

classification physics.soc-ph cond-mat.stat-mechcs.SI

keywords modelanalyticallynetworksprocessessolvableclassequationnetwork

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We introduce a broad class of analytically solvable processes on networks. In the special case, they reduce to random walk and consensus process - two most basic processes on networks. Our class differs from previous models of interactions (such as stochastic Ising model, cellular automata, infinite particle system, and voter model) in several ways, two most important being: (i) the model is analytically solvable even when the dynamical equation for each node may be different and the network may have an arbitrary finite graph and influence structure; and (ii) in addition, when local dynamic is described by the same evolution equation, the model is decomposable: the equilibrium behavior of the system can be expressed as an explicit function of network topology and node dynamics

Analytically solvable processes on networks

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