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.
van Engelenburg, C
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
A partial reversal of the Simon-Lieb inequality is shown for high-dimensional percolation, implying uniform boundedness of phi_pc(S) and several critical estimates.
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.
-
On reversing the Simon-Lieb inequality in high-dimensional percolation
A partial reversal of the Simon-Lieb inequality is shown for high-dimensional percolation, implying uniform boundedness of phi_pc(S) and several critical estimates.