A stationary random graph of no growth rate
Adam Timar
TL;DR
This paper constructs a special random subgraph of a Cayley graph that is invariant under isometries, demonstrating that its exponential growth rate does not exist with probability 1, challenging assumptions about growth rate stability.
Contribution
It introduces a novel invariant subgraph of Cayley graphs exhibiting non-existence of exponential growth rate almost surely.
Findings
The subgraph is isometry-invariant.
The exponential growth rate does not exist with probability 1.
Challenges existing beliefs about growth rate stability in random graphs.
Abstract
We present a random isometry-invariant subgraph of a Cayley graph such that with probability 1 its exponential growth rate does not exist.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Advanced Graph Theory Research · Complex Network Analysis Techniques