Approximately Jumping Towards the Origin
Alex Albors, Fran\c{c}ois Cl\'ement, Shosuke Kiami, Braeden Sodt, Ding, Yifan, Tony Zeng

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Abstract
Given an initial point and a sequence of vectors in , we define a greedy sequence by setting where the sign is chosen so as to minimize . We prove that if the vectors are chosen uniformly at random from then elements of the sequence are, on average, approximately at distance from the origin. We show that the sequence has an invariant measure depending only on and we determine its mean and study its decay for all . We also investigate a completely deterministic example in where the are derived from the van der Corput sequence. Several additional examples are considered.
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TopicsCellular Automata and Applications
