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The group G acts on the space X of infinite paths of the associated graph by changing initial edges of paths.
The unit space ofGis the space of one sided infinite paths inG, andG is the reduction ofGto the space of paths emanating from a distinguished vertex ★.
Guided by their work on KMS states for Toeplitz Cuntz Krieger type algebras associated to infinite matrices, we obtain complete descriptions of the convex sets of KMS states of finite type and of KMS states of infinite type whose associated measures are supported on recurrent infinite paths.
For this reason, we consider infinite paths.
Assume K ∞ is a complex containing no infinite paths.
A spread is essentially a countably branching tree labelled with natural numbers or other finite objects and containing only infinite paths.
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We consider partially observable Markov decision processes (POMDPs) with limit-average payoff, where a reward value in the interval [0,1] is associated with every transition, and the payoff of an infinite path is the long-run average of the rewards.
But that is not an infinite path.
Let c be a closed path in E. Then c c c ⋯ is an infinite path in E, denoted by c ∞, and called a cyclic infinite path.
In fact, B⊆E G) is an infinite path whenever there is a finite path between any of its two vertices.
For any directed (infinite) path θ = e 1 e 2 ⋯ in G ′, a tiling is constructed as follows.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com