$SLE_6$ and 2-d critical bond percolation on the square lattice
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929633728921600 |
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| author | Zhou, Wang |
| author_facet | Zhou, Wang |
| contents | Through the rotational invariance of the 2-d critical bond percolation exploration path on the square lattice we express Smirnov's edge parafermionic observable as a sum of two new edge observables. With the help of these two new edge observables we can apply the discrete harmonic analysis and conformal mapping theory to prove the convergence of the 2-d critical bond percolation exploration path on the square lattice to the trace of $SLE_6$ as the mesh size of the lattice tends to zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03235 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $SLE_6$ and 2-d critical bond percolation on the square lattice Zhou, Wang Probability Mathematical Physics Complex Variables 82B27, 60K35, 82B43, 60D05, 30C35 Through the rotational invariance of the 2-d critical bond percolation exploration path on the square lattice we express Smirnov's edge parafermionic observable as a sum of two new edge observables. With the help of these two new edge observables we can apply the discrete harmonic analysis and conformal mapping theory to prove the convergence of the 2-d critical bond percolation exploration path on the square lattice to the trace of $SLE_6$ as the mesh size of the lattice tends to zero. |
| title | $SLE_6$ and 2-d critical bond percolation on the square lattice |
| topic | Probability Mathematical Physics Complex Variables 82B27, 60K35, 82B43, 60D05, 30C35 |
| url | https://arxiv.org/abs/2409.03235 |