论文标题
对四维统一树的亚历山大 - 奥尔巴赫猜想的对数校正
Logarithmic corrections to the Alexander-Orbach conjecture for the four-dimensional uniform spanning tree
论文作者
论文摘要
我们将精确的对数校正计算到亚历山大 - 孔道行为，以描述四维均匀跨化树的几何和光谱特性的各种数量。特别是，我们证明，树上固有的$ n $ - 球的体积为$ n^2（\ log n）^{ - 1/3+o（1）} $，即$ n $ step随机步行的典型固有位移是$ n^{1/3}（1/3}（1/3}（\ log n）（\ log n）^概率， AS $ n^{ - 2/3}（\ log n）^{1/9-o（1）} $。
We compute the precise logarithmic corrections to Alexander-Orbach behaviour for various quantities describing the geometric and spectral properties of the four-dimensional uniform spanning tree. In particular, we prove that the volume of an intrinsic $n$-ball in the tree is $n^2 (\log n)^{-1/3+o(1)}$, that the typical intrinsic displacement of an $n$-step random walk is $n^{1/3} (\log n)^{1/9-o(1)}$, and that the $n$-step return probability of the walk decays as $n^{-2/3}(\log n)^{1/9-o(1)}$.
