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math.PR2026
A random walk approach to high-dimensional critical phenomena
Hugo Duminil-Copin, Aman Markar, Romain Panis +1
We present a "black box" proof of mean-field near-critical behaviour for a family of functions on () satisfying a short list of assumptions. The functions repr…
math.PR2026
Crossover from subcritical to critical decay: random walk, self-avoiding walk, percolation
Yucheng Liu, Gordon Slade
The study of the Ornstein--Zernike decay of subcritical two-point functions in equilibrium statistical mechanics has a history going back over a century. Despite this, the crossove…