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The universal relation between scaling exponents in first-passage percolation

Probability 2012-08-21 v3 Mathematical Physics math.MP

Abstract

It has been conjectured in numerous physics papers that in ordinary first-passage percolation on integer lattices, the fluctuation exponent χ\chi and the wandering exponent ξ\xi are related through the universal relation χ=2ξ1\chi=2\xi -1, irrespective of the dimension. This is sometimes called the KPZ relation between the two exponents. This article gives a rigorous proof of this conjecture assuming that the exponents exist in a certain sense.

Cite

@article{arxiv.1105.4566,
  title  = {The universal relation between scaling exponents in first-passage percolation},
  author = {Sourav Chatterjee},
  journal= {arXiv preprint arXiv:1105.4566},
  year   = {2012}
}

Comments

33 pages, 8 figures. To appear in the Annals of Math

R2 v1 2026-06-21T18:11:18.527Z