# The Symplectic Size of a Randomly Rotated Convex Body

## TL;DR

This paper investigates the average symplectic capacities of centrally symmetric convex bodies in phase space under random rotations, providing insights into their geometric and symplectic properties.

## Contribution

It introduces a novel analysis of symplectic capacities for convex bodies subjected to random rotations, expanding understanding in symplectic geometry.

## Key findings

- Derived expected values of symplectic capacities for random rotations
- Established bounds and properties of symplectic capacities in this context
- Enhanced understanding of symplectic invariants for convex bodies

## Abstract

In this note we study the expected value of certain symplectic capacities of randomly rotated centrally symmetric convex bodies in the classical phase space.