Power-law bounds for critical long-range percolation below the upper-critical dimension
From MaRDI portal
Publication:2052709
DOI10.1007/s00440-021-01043-7zbMath1475.60200arXiv2008.11197OpenAlexW3171701759MaRDI QIDQ2052709
Publication date: 26 November 2021
Published in: Probability Theory and Related Fields (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2008.11197
Interacting random processes; statistical mechanics type models; percolation theory (60K35) Critical phenomena in equilibrium statistical mechanics (82B27)
Related Items (10)
Sharp hierarchical upper bounds on the critical two-point function for long-range percolation on Zd ⋮ Spatial networks and percolation. Abstracts from the workshop held January 17--23, 2021 (hybrid meeting) ⋮ Recurrence versus transience for weight-dependent random connection models ⋮ On the derivation of mean-field percolation critical exponents from the triangle condition ⋮ Continuity of the Ising phase transition on nonamenable groups ⋮ On the two-point function of the Ising model with infinite-range interactions ⋮ The critical two-point function for long-range percolation on the hierarchical lattice ⋮ An upper bound for \(p_c\) in range-\(R\) bond percolation in two and three dimensions ⋮ Distances in \(\frac{1}{\|x-y\|^{2d}}\) percolation models for all dimensions ⋮ On the radius of Gaussian free field excursion clusters
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model
- Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters
- Locality of the critical probability for transitive graphs of exponential growth
- Percolation in half-spaces: Equality of critical densities and continuity of the percolation probability
- A lower bound on the two-arms exponent for critical percolation on the lattice
- Amenability, unimodularity, and the spectral radius of random walks on infinite graphs
- Mean-field critical behaviour for percolation in high dimensions
- Mean-field behavior for long- and finite range Ising model, percolation and self-avoiding walk
- The growth of the infinite long-range percolation cluster
- Analyticity properties and power law estimates of functions in percolation theory
- Tree graph inequalities and critical behavior in percolation models
- One dimensional \(1/| j-i| ^ s\) percolation models: The existence of a transition for s\(\leq 2\)
- Hyperscaling inequalities for percolation
- The diffusion of self-avoiding random walk in high dimensions
- Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation
- Percolation critical exponents under the triangle condition
- Critical percolation on any nonamenable group has no infinite clusters
- Transience, recurrence and critical behavior for long-range percolation
- Critical exponents for two-dimensional percolation
- Lace expansion for dummies
- Critical two-point function for long-range \(O(n)\) models below the upper critical dimension
- Critical exponents for long-range \(\mathrm O(n)\) models below the upper critical dimension
- On the scaling of the chemical distance in long-range percolation models
- Discontinuity of the percolation density in one dimensional \(1/| x- y| ^ 2\) percolation models
- Scaling relations for 2D-percolation
- Sharpness of the phase transition in percolation models
- Strict inequalities for some critical exponents in two-dimensional percolation
- One-arm exponent for critical 2D percolation
- Critical two-point functions and the lace expansion for spread-out high-dimensional percolation and related models.
- The random-cluster model on the complete graph
- Upper bounds on the percolation correlation length
- Critical two-point function for long-range models with power-law couplings: the marginal case for \({d\ge d_{\mathrm{c}}}\)
- Progress in high-dimensional percolation and random graphs
- Supercritical percolation on nonamenable graphs: isoperimetry, analyticity, and exponential decay of the cluster size distribution
- Every countable infinite group admits a long range percolation with a phase transition
- The crossover region between long-range and short-range interactions for the critical exponents
- Critical two-point functions for long-range statistical-mechanical models in high dimensions
- The lace expansion and its application. École d'Été de Probabilités de Saint-Flour XXXIV -- 2004.
- On the number of incipient spanning clusters
- Mean-field behavior for nearest-neighbor percolation in \(d>10\)
- Annealed scaling relations for Voronoi percolation
- Existence of phase transition for percolation using the Gaussian free field
- New critical exponent inequalities for percolation and the random cluster model
- Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits
- Absence of Infinite Cluster for Critical Bernoulli Percolation on Slabs
- Probability on Trees and Networks
- The supercritical phase of percolation is well behaved
- Inequalities with applications to percolation and reliability
- Percolation
- Sharp asymptotic for the chemical distance in long‐range percolation
- A scaling theory for the long-range to short-range crossover and an infrared duality
- Arm exponents in high dimensional percolation
- The birth of the infinite cluster: Finite-size scaling in percolation
This page was built for publication: Power-law bounds for critical long-range percolation below the upper-critical dimension