Abstract: There has been incredible progress in the last twenty years in the study of fractal paths and fields that arise in planar statistical physics. I will give an introduction to the area and discuss some recent results, focusing on some of the main characters (self-avoiding and loop-erased walk, Brownian loop measures, Schramm–Loewner evolution (SLE) and SLE-type loops, Gaussian free field, Liouville quantum gravity). I will also describe some analogous problems in other spatial dimensions.
https://eta.impa.br/dl/PL009.pdf
本文研究两类共形不变圈测度：第一种为共形不变Brown圈测度和Schramm-Loewner演化(SLE)，然后讨论二维Gauss自由场与量子引力。第二种为SLE型不变圈测度与圈擦除随机游走。应用Loewner微分方程研究SLE需要自然的参数化：SLE_{\kappa}曲线。
相关附件
5-PL009 Lawler.pdf
