Directed Nonabelian Sandpile Models on Trees
Directed Nonabelian Sandpile Models on Trees
复制标题
树木上的定向非阿贝尔沙堆模型
DOI：
10.1007/s00220-015-2343-7
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发表时间：
2013
影响因子：
2.4
通讯作者：
Nicolas M. Thiéry
中科院分区：
文献类型：
--
作者：
Arvind Ayyer;A. Schilling;B. Steinberg;Nicolas M. Thiéry
我们定义了两个一般类的非阿贝尔沙堆模型的有向树（或树形），作为非平衡统计物理模型。与通常应用的阿贝尔沙堆模型不同，这些模型具有沙粒只能通过特定的储层进入的特性。在滴流沙堆模型中，沙粒每次只能移动一个。对于这个模型，我们证明了平稳分布是乘积形式的。在滑坡沙堆模型中，一个顶点上的所有颗粒立即倾倒，这里我们证明了所有特征值的公式，它们的重数和收敛到平稳性的速度。证明使用圈积和幺半群的表示理论。
We define two general classes of nonabelian sandpile models on directed trees (or arborescences), as models of nonequilibrium statistical physics. Unlike usual applications of the well-known abelian sandpile model, these models have the property that sand grains can enter only through specified reservoirs.In the Trickle-down sandpile model, sand grains are allowed to move one at a time. For this model, we show that the stationary distribution is of product form. In the Landslide sandpile model, all the grains at a vertex topple at once, and here we prove formulas for all eigenvalues, their multiplicities, and the rate of convergence to stationarity. The proofs use wreath products and the representation theory of monoids.