Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamical correlation functions for products of random matrices   We introduce and study a family of random processes with a discrete time
related to products of random matrices. Such processes are formed by singular
values of random matrix products, and the number of factors in a random matrix
product plays a role of a discrete time. We consider in detail the case when
the (squared) singular values of the initial random matrix form a polynomial
ensemble, and the initial random matrix is multiplied by standard complex
Gaussian matrices. In this case we show that the random process is a
discrete-time determinantal point process. For three special cases (the case
when the initial random matrix is a standard complex Gaussian matrix, the case
when it is a truncated unitary matrix, or the case when it is a standard
complex Gaussian matrix with a source) we compute the dynamical correlations
functions explicitly, and find the hard edge scaling limits of the correlation
kernels. The proofs rely on the Eynard-Mehta theorem, and on contour integral
representations for the correlation kernels suitable for an asymptotic
analysis.

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The categories of this paper are: quant-ph
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The categories of this paper are: physics
34
The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an