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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

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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Preprints, Working Papers, ...
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https://hal-cea.archives-ouvertes.fr/cea-01198674
Contributor : Emmanuelle de Laborderie <>
Submitted on : Monday, September 14, 2015 - 11:03:23 AM
Last modification on : Wednesday, September 12, 2018 - 2:13:58 PM

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  • HAL Id : cea-01198674, version 1
  • ARXIV : 1405.5244

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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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