## The Annals of Probability

- Ann. Probab.
- Volume 16, Number 1 (1988), 180-188.

### Gaussian Processes and Almost Spherical Sections of Convex Bodies

#### Abstract

We present a simple proof with sharp estimates of Dvoretzky's theorem on the existence of almost spherical sections having large dimension in arbitrary convex bodies in $R^N$.

#### Article information

**Source**

Ann. Probab., Volume 16, Number 1 (1988), 180-188.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176991893

**Digital Object Identifier**

doi:10.1214/aop/1176991893

**Mathematical Reviews number (MathSciNet)**

MR920263

**Zentralblatt MATH identifier**

0639.60046

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60G15: Gaussian processes

Secondary: 46B20: Geometry and structure of normed linear spaces 60B11: Probability theory on linear topological spaces [See also 28C20] 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

**Keywords**

Gaussian processes convex bodies normed spaces random linear maps

#### Citation

Gordon, Yehoram. Gaussian Processes and Almost Spherical Sections of Convex Bodies. Ann. Probab. 16 (1988), no. 1, 180--188. doi:10.1214/aop/1176991893. https://projecteuclid.org/euclid.aop/1176991893