非对称湮灭过程的谱
The spectrum of an asymmetric annihilation process
摘要：
在最近的非平衡统计物理研究中，Ayyer和Mallick研究了一种称为非对称湮灭过程的马尔可夫排斥模型。在它，他们给出了一个精确的猜想的特征值（随着多重性）的转移阵。他们进一步推测，每个本征值只对应一个本征向量。我们证明了第一个这些aesturtures通过引入额外的参数，明确计算其特征值，并表明，新的矩阵减少到原来的一个适当的专业化推广原来的马尔可夫矩阵。此外，我们概述了推导的分拆函数的广义模型，这也减少到一个由Ayyer和Mallick在原来的模型。
英文摘要：
In recent work on nonequilibrium statistical physics, a certain Markovian exclusion model called an asymmetric annihilation process was studied by Ayyer and Mallick. In it they gave a precise conjecture for the eigenvalues (along with the multiplicities) of the transition matrix. They further conjectured that to each eigenvalue, there corresponds only one eigenvector. We prove the first of these conjectures by generalizing the original Markov matrix by introducing extra parameters, explicitly calculating its eigenvalues, and showing that the new matrix reduces to the original one by a suitable specialization. In addition, we outline a derivation of the partition function in the generalized model, which also reduces to the one obtained by Ayyer and Mallick in the original model.
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