Parameter Symmetry in Perturbed GUE Corners Process and Reflected Drifted Brownian Motions
Parameter Symmetry in Perturbed GUE Corners Process and Reflected Drifted Brownian Motions
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DOI：
10.1007/s10955-020-02652-7
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发表时间：
2019-12
影响因子：
1.6
通讯作者：
L. Petrov;M. Tikhonov
中科院分区：
文献类型：
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作者：
L. Petrov;M. Tikhonov
扰动GUE角系综是矩阵的所有主子矩阵特征值的联合分布，其中G是来自高斯酉系综(GUE)的随机矩阵，并且是固定对角矩阵。我们引入基于特征值指数跳跃的马尔可夫转移，并表明它们的连续应用在分布上等效于矩阵的确定性移位。这一结果还为一系列反射布朗运动带来了新的分布对称性，其漂移来自算术级数。我们提出的结构可以被视为第一作者和 Axel Saenz [17] 最近结果的随机矩阵类似物。
The perturbed GUE corners ensemble is the joint distribution of eigenvalues of all principal submatrices of a matrix, whereGis the random matrix from the Gaussian Unitary Ensemble (GUE), andis a fixed diagonal matrix. We introduce Markov transitions based on exponential jumps of eigenvalues, and show that their successive application is equivalent in distribution to a deterministic shift of the matrix. This result also leads to a new distributional symmetry for a family of reflected Brownian motions with drifts coming from an arithmetic progression. The construction we present may be viewed as a random matrix analogue of the recent results of the first author and Axel Saenz [17].