Renormalized energy and asymptotic expansion of optimal logarithmic energy on the sphere

• Verfasst von: Bétermin, Laurent [VerfasserIn]
• Titel: Renormalized energy and asymptotic expansion of optimal logarithmic energy on the sphere
• Mitwirkende: Sandier, Etienne
• Verf.angabe: Laurent Bétermin, Etienne Sandier
• Jahr: 2018
• Jahr des Originals: 2016
• Umfang: 36 S.
• Fussnoten: Gesehen am 14.08.2019 ; Published online: 15 September 2016
• Titel Quelle: Enthalten in: Constructive approximation
• Ort Quelle: New York, NY : Springer, 1985
• Jahr Quelle: 2018
• Band/Heft Quelle: 47(2018), 1, Seite 39-74
• ISSN Quelle: 1432-0940
• DOI: doi:10.1007/s00365-016-9357-z
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 31C20
• Sach-SW: 82B05
• Sach-SW: 82B21
• Sach-SW: Abrikosov lattices
• Sach-SW: Coulomb gas
• Sach-SW: Crystallization
• Sach-SW: Gamma-convergence
• Sach-SW: Ginzburg–Landau
• Sach-SW: Logarithmic energy
• Sach-SW: Logarithmic potential theory
• Sach-SW: Number theory
• Sach-SW: Primary 52A40
• Sach-SW: Renormalized energy
• Sach-SW: Secondary 41A60
• Sach-SW: Triangular lattice
• Sach-SW: Vortices
• Sach-SW: Weak confinement
• K10plus-PPN: 1671396383

Abstract

We study the Hamiltonian of a two-dimensional log-gas with a confining potential V satisfying the weak growth assumption. Finally, we prove the equivalence between the conjecture of Brauchart Brauchart, Hardin and Saff [Contemp. Math., 578:31-61, 2012] about the value of this term and the conjecture of Sandier and Serfaty [Commun Math Phys. 313(3):635-743, 2012] about the minimality of the triangular lattice for a “renormalized energy” W among configurations of fixed asymptotic density.