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

Benoit Collins; Termeh Kousha; Rafał Kulik; Tomasz Szarek; Karol Życzkowski

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

Probability 2019-02-27 v2 Mathematical Physics math.MP

Authors: Benoit Collins , Termeh Kousha , Rafał Kulik , Tomasz Szarek , Karol Życzkowski

Abstract

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 natural derandomization of the hit and run algorithm applied to generate a sequence of random points covering $X$ uniformly. We prove stability of the Markov chain generated by the proposed algorithm and provide its rate of convergence.

Keywords

convex bodies accessibility derandomization hit and run algorithm Markov chain rate of convergence

Cite

@article{arxiv.1312.7061,
  title  = {The accessibility of convex bodies and derandomization of the hit and run algorithm},
  author = {Benoit Collins and Termeh Kousha and Rafał Kulik and Tomasz Szarek and Karol Życzkowski},
  journal= {arXiv preprint arXiv:1312.7061},
  year   = {2019}
}

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revised version, new title and abstract; 13 pages, 2 figures

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

Abstract

Keywords

Cite

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