Beatrice-Helen Vritsiou

Geometry of the _{}-centroid bodies of an isotropic log-concave measure

We study some geometric properties of the

Bodies with maximal isotropic constant

L_q

_{}-centroid bodies and concentration of mass

-centroid bodies

The thin shell estimate

Z_q(\mu)

Tail estimates for linear functionals

of an isotropic log-concave measure

Information theory and the hyperplane conjecture

\mu

Central limit problem and the thin shell conjecture

on

Approximating the covariance matrix

{\mathbb R}^n

Infimum convolution inequalities and concentration

. For any

Hyperplane conjecture and Bourgain’s upper bound

2\ls q\ls\sqrt{n}