The dimension of the Incipient Infinite Cluster
Wouter Cames van Batenburg

TL;DR
This paper investigates the geometric properties of the Incipient Infinite Cluster in high-dimensional percolation, establishing that its mass dimension is almost surely 4 and its volume growth exponent is almost surely 2.
Contribution
It provides rigorous proofs that the mass dimension and volume growth exponent of the IIC are almost surely 4 and 2 respectively in high dimensions.
Findings
Mass dimension of IIC is almost surely 4.
Volume growth exponent of IIC is almost surely 2.
Results hold for high-dimensional bond percolation on z^d.
Abstract
We study the Incipient Infinite Cluster (IIC) of high-dimensional bond percolation on . We prove that the mass dimension of IIC almost surely equals and the volume growth exponent of IIC almost surely equals .
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Taxonomy
TopicsStochastic processes and statistical mechanics · advanced mathematical theories · Mathematical Dynamics and Fractals
