solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看6060次
Limits of conformal images and conformal images of limits for planar random curves. (arXiv:1810.05608v1 [math-ph])
来源于:arXiv
Consider a chordal random curve model on a planar graph, in the scaling limit
when a fine-mesh graph approximates a simply-connected planar domain. The
well-known precompactness conditions of Kemppainen and Smirnov show that
certain "crossing estimates" guarantee the subsequential weak convergence of
the random curves in the topology of unparametrized curves, as well as in a
topology inherited from curves on the unit disc via conformal maps. We
complement this result by proving that proceeding to weak limit commutes with
changing topology, i.e., limits of conformal images are conformal images of
limits, without imposing any boundary regularity assumptions on the domains
where the random curves lie. Treating such rough boundaries becomes necessary,
e.g., in convergence proofs to multiple SLEs. The result in this generality has
not been explicated before and is not trivial, which we demonstrate by giving
warning examples and deducing strong consequences. 查看全文>>