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- W3124458885 abstract "The random variable $1+z_1+z_1z_2+dots$ appears in many contexts and was shown by Kesten to exhibit a heavy tail distribution. We consider natural extensions of this variable and its associated recursion to $N times N$ matrices either real symmetric $beta=1$ or complex Hermitian $beta=2$. In the continuum limit of this recursion, we show that the matrix distribution converges to the inverse-Wishart ensemble of random matrices. The full dynamics is solved using a mapping to $N$ fermions in a Morse potential, which are non-interacting for $beta=2$. At finite $N$ the distribution of eigenvalues exhibits heavy tails, generalizing Kesten's results in the scalar case. The density of fermions in this potential is studied for large $N$, and the power-law tail of the eigenvalue distribution is related to the properties of the so-called determinantal Bessel process which describes the hard edge universality of random matrices. For the discrete matrix recursion, using free probability in the large $N$ limit, we obtain a self-consistent equation for the stationary distribution. The relation of our results to recent works of Rider and Valk'o, Grabsch and Texier, as well as Ossipov, is discussed." @default.
- W3124458885 created "2021-02-01" @default.
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- W3124458885 date "2021-05-31" @default.
- W3124458885 modified "2023-10-17" @default.
- W3124458885 title "Matrix Kesten recursion, inverse-Wishart ensemble and fermions in a Morse potential" @default.
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- W3124458885 doi "https://doi.org/10.1088/1751-8121/abfc7f" @default.
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