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Conformal invariance in two-dimensional percolation. (English) Zbl 0794.60109
The paper describes very concretely, although in hypothetical form, the geometric aspects of universality, especially conformal invariance, in the context of percolation, and presents the numerical results that support the hypothesis. An attractive feature of the paper is nonformal description of some mathematical problems posed by the physical notations. The description of all concepts introduced in the paper is essential in order to establish their physical importance and to clarify their mathematical contents. The paper orients inexperienced mathematicians with respect to the physical background.
In order to provide some evidence for the hypotheses of universality and conformal invariance the paper contains a description of several simulations, including experimental verification of Cardi’s formula. Some precise basic definitions are necessary simply to orient the reader. No theorems are proved or implied.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation
82B27 Critical phenomena in equilibrium statistical mechanics
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