约束测度的桥分解
Bridge Decomposition of Restriction Measures
摘要：
受Kesten的桥分解的启发，在上半平面的二维自避免行走，我们表明，半平面SAW，SLE（8/3）过程的限制标度极限，也有一个适当定义的桥分解。这种连续分解完全是SLE（8/3）的限制性质的结果，因此可以推广到更广泛的限制测度类。具体地说，我们表明，限制壳指数小于1可以分解成一个泊松点过程的不可约桥的方式是类似于伊藤的布朗运动根据其零点的行程分解。
英文摘要：
Motivated by Kesten's bridge decomposition for two-dimensional self-avoiding walks in the upper half plane, we show that the conjectured scaling limit of the half-plane SAW, the SLE(8/3) process, also has an appropriately defined bridge decomposition. This continuum decomposition turns out to entirely be a consequence of the restriction property of SLE(8/3), and as a result can be generalized to the wider class of restriction measures. Specifically we show that the restriction hulls with index less than one can be decomposed into a Poisson Point Process of irreducible bridges in a way that is similar to Ito's excursion decomposition of a Brownian motion according to its zeros.
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