Excursion decompositions for SLE and Watts' crossing formula
Excursion decompositions for SLE and Watts' crossing formula
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SLE 和瓦茨交叉公式的偏移分解
DOI：
10.1007/s00440-005-0446-3
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发表时间：
2004
影响因子：
2
通讯作者：
Julien Dubédat
中科院分区：
文献类型：
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作者：
Julien Dubédat
Schramm-Loewner演化(SLEs)具有A.S.如果κ>；4和A.S.如果4<；κ<；8.如果κ&>4，则适当版本的SLE(κ)具有更新特性：在访问其边界之后重新开始。因此，人们可以对这种特殊的系统性红斑狼疮(κ)“远离它的边界”进行漂移分解。对于4<；κ<；8，这种情况有一个双向的类比：一个特定版本的κ具有一个更新性质，即它的切点；人们研究这个SLE“远离它的切点”的游程分解。对于κ=6，这与Virág关于“布朗珠子”的结果重叠。作为这种构造的副产品，我们证明了Watts公式，该公式描述了临界平面渗流中矩形内双重交叉的概率。
It is known that Schramm-Loewner Evolutions (SLEs) have a.s. frontier points if κ>4 and a.s. cutpoints if 4<κ<8. If κ>4, an appropriate version of SLE(κ) has a renewal property: it starts afresh after visiting its frontier. Thus one can give an excursion decomposition for this particular SLE(κ) “away from its frontier”. For 4<κ<8, there is a two-sided analogue of this situation: a particular version of SLE(κ) has a renewal property w.r.t its cutpoints; one studies excursion decompositions of this SLE “away from its cutpoints”. For κ=6, this overlaps Virág's results on “Brownian beads”. As a by-product of this construction, one proves Watts' formula, which describes the probability of a double crossing in a rectangle for critical plane percolation.