Convergence of $k$-point functions in high dimensional percolation
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914461810425856 |
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| author | Chatterjee, Shirshendu Chinmay, Pranav Hanson, Jack Sosoe, Philippe |
| author_facet | Chatterjee, Shirshendu Chinmay, Pranav Hanson, Jack Sosoe, Philippe |
| contents | Consider critical Bernoulli percolation on $\mathbb{Z}^d$ for $d$ large; let $y_0, \dots, y_{k-1}$ be $k$ distinct points in $\mathbb{R}^d$. We prove that the probability that $\{\lfloor n y_i\rfloor\}_{i=0}^{k-1}$ all lie in the same open cluster, rescaled by an appropriate power of $n$, converges as $n \to \infty$ to an explicit constant. This confirms a conjecture of Aizenman and Newman. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08462 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergence of $k$-point functions in high dimensional percolation Chatterjee, Shirshendu Chinmay, Pranav Hanson, Jack Sosoe, Philippe Probability 60K35, 82B43 Consider critical Bernoulli percolation on $\mathbb{Z}^d$ for $d$ large; let $y_0, \dots, y_{k-1}$ be $k$ distinct points in $\mathbb{R}^d$. We prove that the probability that $\{\lfloor n y_i\rfloor\}_{i=0}^{k-1}$ all lie in the same open cluster, rescaled by an appropriate power of $n$, converges as $n \to \infty$ to an explicit constant. This confirms a conjecture of Aizenman and Newman. |
| title | Convergence of $k$-point functions in high dimensional percolation |
| topic | Probability 60K35, 82B43 |
| url | https://arxiv.org/abs/2604.08462 |