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Scaling limits of two‐dimensional percolation: an overview
Author(s) -
Camia Federico
Publication year - 2008
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2008.00400.x
Subject(s) - scaling , scaling limit , percolation (cognitive psychology) , statistical physics , limit (mathematics) , mathematics , convergence (economics) , percolation critical exponents , cluster (spacecraft) , critical exponent , mathematical analysis , computer science , physics , geometry , neuroscience , economics , biology , programming language , economic growth
We present a review of the recent progress on percolation scaling limits in two dimensions. In particular, we consider the convergence of critical crossing probabilities to Cardy's formula and of the critical exploration path to chordal stochastic Loewner evolution (SLE 6 ), the full scaling limit of critical cluster boundaries, and near‐critical scaling limits.