On the scaling of the chemical distance in long-range percolation models
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Publication:1769503
DOI10.1214/009117904000000577zbMath1072.60084arXivmath/0304418OpenAlexW2065630310MaRDI QIDQ1769503
Publication date: 21 March 2005
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0304418
Interacting random processes; statistical mechanics type models; percolation theory (60K35) Renormalization group methods in equilibrium statistical mechanics (82B28) Percolation (82B43)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Gaussian fluctuations of connectivities in the subcritical regime of percolation
- The Wulff construction and asymptotics of the finite cluster distribution for two-dimensional Bernoulli percolation
- One dimensional \(1/| j-i| ^ s\) percolation models: The existence of a transition for s\(\leq 2\)
- Density and uniqueness in percolation
- Uniqueness of the infinite component in a random graph with applications to percolation and spin glasses
- The scaling limit of the incipient infinite cluster in high-dimensional percolation. I: Critical exponents
- Transience, recurrence and critical behavior for long-range percolation
- Critical exponents for two-dimensional percolation
- Geometry of the uniform spanning forest: transitions in dimensions 4, 8, 12,\dots
- Discontinuity of the percolation density in one dimensional \(1/| x- y| ^ 2\) percolation models
- Sharpness of the phase transition in percolation models
- Ornstein-Zernike theory for the Bernoulli bond percolation on \(\mathbb Z^d\)
- On the chemical distance for supercritical Bernoulli percolation
- The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion
- Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits
- The diameter of long-range percolation clusters on finite cycles
- The diameter of a long-range percolation graph
- The supercritical phase of percolation is well behaved
- Collective dynamics of ‘small-world’ networks
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