一类带结构随机矩阵的渗流
Percolation in a Class of Band Structured Random Matrices
摘要：
我们定义了一类属于随机环状聚合物的随机矩阵系综。这种无规环状聚合物是生物聚合物如细胞核中的染色质的可能模型。结果表明，最大特征值$λ_{max}$的分布依赖于随机矩阵的项中的渗流跃迁。在渗流阈值以下，分布是多峰的，并且在阈值以上改变为Tracy-Widom分布。我们还表明，本征值的分布既不是维格纳形式，也不是高斯。
英文摘要：
We define a class of random matrix ensembles that pertain to random looped polymers. Such random looped polymers are a possible model for bio-polymers such as chromatin in the cell nucleus. It is shown that the distribution of the largest eigenvalue $λ_{max}$ depends on a percolation transition in the entries of the random matrices. Below the percolation threshold the distribution is multi-peaked and changes above the threshold to the Tracy-Widom distribution. We also show that the distribution of the eigenvalues is neither of the Wigner form nor gaussian.
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