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SAMPLING CONVEX BODIES: A RANDOM MATRIX APPROACH GUILLAUME AUBRUN
 

Summary: 



SAMPLING CONVEX BODIES: A RANDOM MATRIX APPROACH



GUILLAUME AUBRUN



Abstract.We prove the following result: for any " > 0, only C(")n sample *
*points are enough to
obtain (1+")-approximation of the inertia ellipsoid of an unconditional c*
*onvex body in Rn. Moreover,
for any ae > 1, already aen sample points give isomorphic approximation o*
*f the inertia ellipsoid. The
proofs rely on an adaptation of the moments method from the Random Matrix*
* Theory.

  

Source: Aubrun, Guillaume - Institut Camille Jordan, Université Claude Bernard Lyon-I

 

Collections: Mathematics