|
A conformal loop ensemble (CLEκ) is a random collection of non-crossing loops in a simply connected, open subset of the plane. These random collections of loops are indexed by a parameter κ, which may be any real number between 8/3 and 8. CLEκ is a loop version of the Schramm-Loewner evolution: SLEκ is designed to model a single discrete random interface, while CLEκ models a full collection of interfaces. In many instances for which there is a conjectured or proved relationship between a discrete model and SLEκ, there is also a conjectured or proved relationship with CLEκ. For example: *CLE3 is the limit of interfaces for the critical Ising model. *CLE4 may be viewed as a set of level lines of the Gaussian free field. *CLE16/3 is a scaling limit of cluster interfaces in critical FK percolation. *CLE6 is a scaling limit of critical percolation on the triangular lattice. ==Constructions== For 8/3 < κ < 8, CLEκ may be constructed using a branching variation of an SLEκ process (). When 8/3 < κ ≤ 4, CLEκ may be alternatively constructed as the collection of outer boundaries of Brownian loop soup clusters (). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Conformal loop ensemble」の詳細全文を読む スポンサード リンク
|