Geodesic
On the derivation of the homogeneous kinetic wave equation for a nonlinear random matrix model
Ars Inveniendi Analytica (2023).

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We consider a nonlinear system of ODEs, where the underlying linear dynamics are determined by a Hermitian random matrix ensemble. We prove that the leading order dynamics in the weakly nonlinear, infinite volume limit are determined by a solution to the corresponding kinetic wave equation on a non-trivial timescale. Our proof relies on estimates for Haar-distributed unitary matrices obtained from Weingarten calculus, which may be of independent interest.
Publié le :
DOI : 10.15781/kj6t-gd51 
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     author = {Guillaume Dubach and Pierre Germain and Benjamin Harrop-Griffiths},
     title = {On the derivation of the homogeneous kinetic wave equation for a
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Guillaume Dubach; Pierre Germain; Benjamin Harrop-Griffiths. On the derivation of the homogeneous kinetic wave equation for a
  nonlinear random matrix model. Ars Inveniendi Analytica (2023). doi : 10.15781/kj6t-gd51. http://geodesic.mathdoc.fr/articles/10.15781/kj6t-gd51/

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