A note on percolation in cocycle measures
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Publication:5307894
DOI10.1214/074921706000000059zbMATH Open1125.82006arXivmath/0608217OpenAlexW3101376493MaRDI QIDQ5307894
Publication date: 19 September 2007
Abstract: We describe infinite clusters which arise in nearest-neighbour percolation for so-called cocycle measures on the square lattice. These measures arise naturally in the study of random transformations. We show that infinite clusters have a very specific form and direction. In concrete situations, this leads to a quick decision whether or not a certain cocycle measure percolates. We illustrate this with two examples which are interesting in their own right.
Full work available at URL: https://arxiv.org/abs/math/0608217
Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)
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