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.
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Adele-valued random walks converge weakly to an adelic Lévy process in the J1 Skorokhod topology after appropriate scaling.
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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.
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A Scaling Limit of Random Walks in the Rational Adeles
Adele-valued random walks converge weakly to an adelic Lévy process in the J1 Skorokhod topology after appropriate scaling.