Cycle structure of percolation on high-dimensional tori
From MaRDI portal
Publication:405505
DOI10.1214/13-AIHP565zbMath1297.05222arXiv1109.1233MaRDI QIDQ405505
Artëm Sapozhnikov, Remco van der Hofstad
Publication date: 5 September 2014
Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1109.1233
Random graphs (graph-theoretic aspects) (05C80) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Combinatorial probability (60C05) Percolation (82B43)
Related Items
The survival probability and \(r\)-point functions in high dimensions, Subcritical connectivity and some exact tail exponents in high dimensional percolation, On breadth‐first constructions of scaling limits of random graphs and random unicellular maps, The near-critical two-point function and the torus plateau for weakly self-avoiding walk in high dimensions, High-dimensional near-critical percolation and the torus plateau, Scaling limits for the threshold window: when does a monotone Boolean function flip its outcome?, Random walk on the high-dimensional IIC, Geometry of the minimal spanning tree of a random 3-regular graph, Universal finite-size scaling for percolation theory in high dimensions
Cites Work
- Unnamed Item
- Hypercube percolation
- Critical random graphs: limiting constructions and distributional properties
- Random graph asymptotics on high-dimensional tori. II: volume, diameter and mixing time
- Random subgraphs of finite graphs. III: The phase transition for the \(n\)-cube
- Random graph asymptotics on high-dimensional tori
- Mean-field critical behaviour for percolation in high dimensions
- Critical random graphs: Diameter and mixing time
- The Alexander-Orbach conjecture holds in high dimensions
- On the upper critical dimension of Bernoulli percolation
- The critical probability of bond percolation on the square lattice equals 1/2
- Brownian excursions, critical random graphs and the multiplicative coalescent
- Critical two-point functions and the lace expansion for spread-out high-dimensional percolation and related models.
- Decay of correlations in nearest-neighbor self-avoiding walk, percolation, lattice trees and animals
- Random subgraphs of finite graphs. II: The lace expansion and the triangle condition
- Percolation
- The Structure of a Random Graph at the Point of the Phase Transition
- The birth of the giant component
- Random subgraphs of finite graphs: I. The scaling window under the triangle condition
- Arm exponents in high dimensional percolation
