Parameter Symmetry in Perturbed GUE Corners Process and Reflected Drifted Brownian Motionsстатья
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Аннотация:The perturbed GUE corners ensemble is the joint distribution of eigenvalues of all principal submatrices of a matrix 𝐺+diag(𝐚), where G is the random matrix from the Gaussian Unitary Ensemble (GUE), and diag(𝐚) is 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].