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We introduce the concept of accessibility and prove that any convex body $X$in $\mathbb R^d$ is accessible with relevant constants depending on $d$ only.This property leads to a new algorithm which may be considered as a naturalderandomization of the hit and run algorithm applied to generate a sequence ofrandom points covering $X$ uniformly. We prove stability of the Markov chaingenerated by the proposed algorithm and provide its rate of convergence.

The accessibility of convex bodies and derandomization of the hit and run algorithm