Critical exponents for a percolation model on transient graphs
Critical exponents for a percolation model on transient graphs
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DOI：
10.1007/s00222-022-01168-z
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发表时间：
2021-01
影响因子：
3.1
通讯作者：
Alexander Drewitz;Alexis Prévost;Pierre-François Rodriguez
中科院分区：
文献类型：
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作者：
Alexander Drewitz;Alexis Prévost;Pierre-François Rodriguez
本文考虑了由电缆系统上高斯自由场的偏移集引起的瞬态加权图上的键渗流问题。由于这种设置的连续性和强大的马尔可夫性质的领域，一方面，和潜在的理论的相关扩散的联系，另一方面，我们严格确定的各种关键量的行为有关的（近）临界制度的这个模型。特别是，我们的结果适用的情况下，基图是三维立方晶格。他们揭示了相关的临界指数的值，这是明确的，但不是平均场，并符合从标度理论的预测低于上临界尺寸。
We consider the bond percolation problem on a transient weighted graph induced by the excursion sets of the Gaussian free field on the corresponding cable system. Owing to the continuity of this setup and the strong Markov property of the field on the one hand, and the links with potential theory for the associated diffusion on the other, we rigorously determine the behavior of various key quantities related to the (near-)critical regime for this model. In particular, our results apply in case the base graph is the three-dimensional cubic lattice. They unveil the values of the associated critical exponents, which are explicit but not mean-field and consistent with predictions from scaling theory below the upper-critical dimension.