Site Percolation on Multi-dimensional Lattice
Marko Puljic
TL;DR
This paper investigates site percolation on infinite multi-dimensional lattices, demonstrating that when sites are open with probability at least 1/d, an infinite open path almost surely exists.
Contribution
It establishes a threshold probability for the emergence of an infinite open path in d-dimensional lattices, extending percolation theory to higher dimensions.
Findings
Infinite open path exists when site probability ≥ 1/d
Threshold probability for percolation in d-dimensions is identified
Results extend classical percolation theory to multi-dimensional lattices
Abstract
Sites in an infinite d-dimensional lattice, open with probability greater or equal to 1/d, form an infinite open path.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Stochastic processes and statistical mechanics