Maximal Fluctuations on Periodic Lattices: An Approach via Quantitative Wulff Inequalities

Marco Cicalese, Gian Paolo Leonardi

Publikation: Beitrag in FachzeitschriftArtikelBegutachtung

9 Zitate (Scopus)

Abstract

We consider the Wulff problem arising from the study of the Heitmann–Radin energy of N atoms sitting on a periodic lattice. Combining the sharp quantitative Wulff inequality in the continuum setting with a notion of quantitative closeness between discrete and continuum energies, we provide very short proofs of fluctuation estimates of Voronoi-type sets associated with almost minimizers of the discrete problem about the continuum limit Wulff shape. In the particular case of exact energy minimizers, we recover the well-known, sharp N3 / 4 scaling law for all considered planar lattices, as well as a sub-optimal scaling law for the cubic lattice in dimension d≥ 3.

OriginalspracheEnglisch
Seiten (von - bis)1931-1944
Seitenumfang14
FachzeitschriftCommunications in Mathematical Physics
Jahrgang375
Ausgabenummer3
DOIs
PublikationsstatusVeröffentlicht - 1 Mai 2020

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