Macrodimension - an invariant of local dynamics
V. A. Malyshev
TL;DR
This paper introduces a Markov process on countable graphs with spins and proves that the scaling macrodimension remains invariant under these local graph transformations.
Contribution
It defines a new Markov process on graphs with spins and establishes the invariance of the scaling macrodimension under local substitutions.
Findings
Scaling macrodimension is invariant under the defined dynamics.
The process involves local substitutions in graphs with spins.
The invariance property holds for countable graphs.
Abstract
We define a Markov process on the set of countable graphs with spins. Transitions are local substitutions in the graph. It is proved that the scaling macrodimension is an invariant of such dynamics.
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Taxonomy
Topicsadvanced mathematical theories · Topological and Geometric Data Analysis · Mathematical Dynamics and Fractals