## Abstract

Kaluža, Kopecká and the author have shown that the best Lipschitz constant for mappings taking a given n

^{d}-element set in the integer lattice ℤ^{d}, with*n*∈ℕ, surjectively to the regular*n*times*n*grid {1,…,*n*}^{d}may be arbitrarily large. However, there remain no known, non-trivial asymptotic bounds, either from above or below, on how this best Lipschitz constant grows with*n*. We approach this problem from a probabilistic point of view. More precisely, we consider the random configuration of*n*^{d }points inside a given finite lattice and establish almost sure, asymptotic upper bounds of order log*n*on the best Lipschitz constant of mappings taking this set surjectively to the regular*n*times*n*grid {1,…,*n*}^{d}.Original language | English |
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Publisher | arXiv |

DOIs | |

Publication status | Published - 28 Oct 2020 |

### Bibliographical note

18 pages## Keywords

- math.FA
- 51F99, 51M05, 52C99, 26B10

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