Diffusion in the space of complex Hermitian matrices - microscopic properties of the averaged characteristic polynomial and the averaged inverse characteristic polynomial - Archive ouverte HAL Access content directly
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Diffusion in the space of complex Hermitian matrices - microscopic properties of the averaged characteristic polynomial and the averaged inverse characteristic polynomial

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Jean-Paul Blaizot
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Jacek Grela
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Maciej A. Nowak
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Piotr Warchoł
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Abstract

We show that the averaged characteristic polynomial and the averaged inverse characteristic polynomial, associated with Hermitian matrices whose elements perform a random walk in the space of complex numbers, satisfy certain partial differential, diffusion-like, equations. These equations are valid for matrices of arbitrary size. Their solutions can be given an integral representation that allows for a simple study of their asymptotic behaviors for a broad range of initial conditions.

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cea-01198674 , version 1 (14-09-2015)

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Jean-Paul Blaizot, Jacek Grela, Maciej A. Nowak, Piotr Warchoł. Diffusion in the space of complex Hermitian matrices - microscopic properties of the averaged characteristic polynomial and the averaged inverse characteristic polynomial. 2015. ⟨cea-01198674⟩
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