A black-box random-walk proof establishes mean-field near-critical decay |x|^{-d+2+ε} exp(-c|x|/ξ) for two-point functions on Z^d (d>2) under a short list of assumptions, covering self-avoiding walk, percolation, Ising, XY, |φ|^4 and lattice trees above their upper critical dimensions.
Duminil-Copin and R
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
math.PR 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Proves that Ornstein-Zernike solutions for random walks, self-avoiding walks in d≥5, and percolation in d≥15 asymptotically match the Green function of drifted Brownian motion multiplied by an anisotropic exponentially decaying factor.
citing papers explorer
-
A random walk approach to high-dimensional critical phenomena
A black-box random-walk proof establishes mean-field near-critical decay |x|^{-d+2+ε} exp(-c|x|/ξ) for two-point functions on Z^d (d>2) under a short list of assumptions, covering self-avoiding walk, percolation, Ising, XY, |φ|^4 and lattice trees above their upper critical dimensions.
-
Crossover from subcritical to critical decay: random walk, self-avoiding walk, percolation
Proves that Ornstein-Zernike solutions for random walks, self-avoiding walks in d≥5, and percolation in d≥15 asymptotically match the Green function of drifted Brownian motion multiplied by an anisotropic exponentially decaying factor.