A Hydrodynamic Exercise in Free Probability: Setting up Free Euler Equations
Operator Algebras
2019-04-25 v3 Analysis of PDEs
Abstract
For the free probability analogue of Euclidean space endowed with the Gaussian measure we apply the approach of Arnold to derive Euler equations for a Lie algebra of non-commutative vector fields which preserve a certain trace. We extend the equations to vector fields satisfying non-commutative smoothness requirements. We introduce a cyclic vorticity and show that it satisfies a vorticity equation and that it produces a family of conserved quantities.
Cite
@article{arxiv.1902.02442,
title = {A Hydrodynamic Exercise in Free Probability: Setting up Free Euler Equations},
author = {Dan-Virgil Voiculescu},
journal= {arXiv preprint arXiv:1902.02442},
year = {2019}
}
Comments
14 pages, preliminary version, made additions to sections 5 and 7, changed sign of commutator, added remarks