Dimensionality and randomness
<|reference_start|>Dimensionality and randomness: Arranging the bits of a random string or real into k columns of a two-dimensional array or higher dimensional structure is typically accompanied with loss in the Kolmogorov complexity of the columns, which depends on k. We quantify and characterize this phenomenon for arrays and trees and its relationship to negligible classes.<|reference_end|>
@article{barmpalias2024dimensionality,
    title={Dimensionality and randomness},
    author={George Barmpalias and Xiaoyan Zhang},
    journal={arXiv preprint arXiv:2405.06961},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.06961},
    primaryClass={math.LO cs.DM cs.IT math.IT}
}