The scaling limit of lattice trees in high dimensions
From MaRDI portal
Publication:1268040
DOI10.1007/s002200050319zbMath0915.60076OpenAlexW2072609575MaRDI QIDQ1268040
Publication date: 13 December 1998
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s002200050319
scaling limitsuper-Brownian motionintegrated super-Brownian excursionnearest-neighbour lattice trees
Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics (82B21) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)
Related Items (31)
Critical two-point functions and the lace expansion for spread-out high-dimensional percolation and related models. ⋮ Excursion theory for Brownian motion indexed by the Brownian tree ⋮ Infinite canonical super-Brownian motion and scaling limits ⋮ The survival probability and \(r\)-point functions in high dimensions ⋮ On the range of lattice models in high dimensions ⋮ Random walk on barely supercritical branching random walk ⋮ Self‐avoiding walk on the hypercube ⋮ The Markov property of local times of Brownian motion indexed by the Brownian tree ⋮ A large deviation theorem for a supercritical super-Brownian motion with absorption ⋮ Historical lattice trees ⋮ Weakly self-avoiding walk on a high-dimensional torus ⋮ Long-range self-avoiding walk converges to \(\alpha\)-stable processes ⋮ Models of random subtrees of a graph ⋮ The lace expansion on a tree with application to networks of self-avoiding walks ⋮ Large deviations under a viewpoint of metric geometry: measure-valued process cases ⋮ An expansion for self-interacting random walks ⋮ Weak convergence of measure-valued processes and \(r\)-point functions ⋮ Random real trees ⋮ The scaling limit of loop-erased random walk in three dimensions ⋮ The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion ⋮ A conditional limit theorem for tree-indexed random walk ⋮ Rescaled Lotka-Volterra models converge to super-Brownian motion ⋮ Transfer current and pattern fields in spanning trees ⋮ NoBLE for lattice trees and lattice animals ⋮ Spatial moments for high-dimensional critical contact process, oriented percolation and lattice trees ⋮ Polygons and the Lace Expansion ⋮ Expansion in High Dimension for the Growth Constants of Lattice Trees and Lattice Animals ⋮ Super-Brownian motion conditioned on the total mass ⋮ Loop-erased random walk on a torus in dimensions 4 and above ⋮ Mean-field lattice trees ⋮ Equivalence of mean-field avalanches and branching diffusions: from the Brownian force model to the super-Brownian motion
This page was built for publication: The scaling limit of lattice trees in high dimensions
