Limit of the Wulff crystal when approaching criticality for site percolation on the triangular lattic (Q743069)
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| Language | Label | Description | Also known as |
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| English | Limit of the Wulff crystal when approaching criticality for site percolation on the triangular lattic |
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Limit of the Wulff crystal when approaching criticality for site percolation on the triangular lattic (English)
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22 September 2014
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Using the techniques of \textit{C. Garban, G. Pete} and \textit{O. Schramm} [``The scaling limits of near-critical and dynamical percolation'', \url{arXiv:1305.5526}], it is proved that the Wulff crystal of the percolation on the regular triangular lattice tends to a Euclidean disk as \(p\) goes to \(p_c\). The main ingredient of the proof is the rotational invariance of the scaling limit of near-critical percolation proved in the mentioned paper.
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planar percolation
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near-critical regime
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inverse correlation length
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Wulff crystal
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