高于一般屏障的真实自避运动
True self-repelling motion above a general barrier
AI总结：
本文研究了在一般屏障上构造的真实自避运动，并探讨了其在不规则屏障下的证明扩展难题。
摘要：
真实自避运动是一种连续时间随机过程，由Tóth和Werner于1998年引入，作为由Tóth于1995年定义的“真实”自避随机游走的极限。真实自避运动的构造涉及从上半平面所有点出发的不可数个共聚布朗运动系统，与布朗网络相关，但被反射并在一个“屏障”上吸收，该屏障是横轴。在本文中，我们考虑更为一般的屏障，构造一个不可数个共聚布朗运动系统，这些布朗运动被反射并在这些屏障上吸收，并与之关联的真实自避运动。将Tóth和Werner的证明扩展到这种更一般情况的扩展出人意料地困难，尤其是当屏障不规则时。
英文摘要：
The true self-repelling motion is a continuous-time random process which was introduced by Tóth and Werner in 1998 to be a limit for the "true" self-avoiding random walk defined by Tóth in 1995. The construction of the true self-repelling motion involves an uncountable system of coalescing Brownian motions starting from all points of the upper half-plane, related to the Brownian web, but reflected and absorbed on a "barrier" which is the abscissa axis. In this work, we consider much more general barriers, construct an uncountable system of coalescing Brownian motions reflected and absorbed on these barriers, and the true self-repelling motion associated to it. The extension of the proofs of Tóth and Werner to this more general case is surprisingly difficult, especially when the barrier is irregular.
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