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• W2184593544 abstract "This paper studies a number of matrix models of size n and the associated Markov chains for the eigenvalues of the models for consecutive n’s. They are consecutive principal minors for two of the models, GUE with external source and the multiple Laguerre matrix model, and merely properly dened consecutive matrices for the third one, the Jacobi-Pi~ neiro model; nevertheless the eigenvalues of the consecutive models all interlace. We show: (i) For each of those nite models, we give the transition probability of the associated Markov chain and the joint distribution of the entire interlacing set of eigenvalues; we show this is a determinantal point process whose extended kernels share many common features. (ii) To each of these models and their set of eigenvalues, we associate a last-passage percolation model, either nite percolation or percolation along an innite strip of nite width, yielding a precise relationship between the last passage times and the eigenvalues. (iii) Finally it is shown that for appropriate choices of exponential distribution on the percolation, with very small means, the rescaled last passage times lead to the Pearcey process; this should connect the Pearcey statistics with random directed polymers." @default.
• W2184593544 created "2016-06-24" @default.
• W2184593544 creator A5070787888 @default.
• W2184593544 date "2013-01-01" @default.
• W2184593544 modified "2023-09-27" @default.
• W2184593544 title "Random matrix minor processes related to percolation theory" @default.
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• W2184593544 hasPublicationYear "2013" @default.
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