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Pré-Publication, Document De Travail Année : 2016

Dynamical invariance for random matrices

Jeremie Unterberger
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Résumé

We consider a general Langevin dynamics for the one-dimensional N-particle Coulomb gas with confining potential V at temperature β. These dynamics describe for β=2 the time evolution of the eigenvalues of N×N random Hermitian matrices. The equilibrium partition function -- equal to the normalization constant of the Laughlin wave function in fractional quantum Hall effect -- is known to satisfy an infinite number of constraints called Virasoro or loop constraints. We introduce here a dynamical generating function on the space of random trajectories which satisfies a large class of constraints of geometric origin. We focus in this article on a subclass induced by the invariance under the Schr\"odinger-Virasoro algebra.
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hal-01304554 , version 1 (19-04-2016)

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  • HAL Id : hal-01304554 , version 1

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Jeremie Unterberger. Dynamical invariance for random matrices. 2016. ⟨hal-01304554⟩
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