论文标题
由非冲洗戴森的布朗尼动作驱动的多个SLE的三个阶段
Three phases of multiple SLE driven by non-colliding Dyson's Brownian motions
论文作者
论文摘要
本文涉及多个由参数$κ\标记的多个schramm的属性（SLE）（0,8] $。具体来说，我们考虑了多个loewner方程的解决方案的解决方案的解决方案驱动了dyson的时间变化，dyson的布朗尼运动的时间变化是由于该属性的几个属性，即在该属性中的多种属性，并且可以通过sap and of sap and of sap的属性来驱动的dys notions。只有在这种限制的情况下，通过换通勤的情况，就不会有多个曲线来克服多个曲线。当$κ\ in（0,4] $，（ii）当$κ\ in（4,8）$和（iii）填充空间曲线时，当$κ= 8 $时相交曲线时。
The present paper is concerned with properties of multiple Schramm--Loewner evolutions (SLEs) labelled by a parameter $κ\in (0,8]$. Specifically, we consider the solution of the multiple Loewner equation driven by a time change of Dyson's Brownian motions in the non-colliding regime. Although it is often considered that several properties of the solution can be studied by means of commutation relations of SLEs and the absolute continuity, this method is available only in the case that the curves generated by commuting SLEs are separated. Beyond this restriction, it is not even obvious that the solution of the multiple Loewner equation generates multiple curves. To overcome this difficulty, we employ the coupling of Gaussian free fields and multiple SLEs. Consequently, we prove the longstanding conjecture that the solution indeed generates multiple continuous curves. Furthermore, these multiple curves are (i) simple disjoint curves when $κ\in (0,4]$, (ii) intersecting curves when $κ\in (4,8)$, and (iii) space-filling curves when $κ=8$.
