Renormalized energy and asymptotic expansion of optimal logarithmic energy on the sphere
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...
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| Other Authors: | |
| Format: | Article (Journal) |
| Language: | English |
| Published: |
2018
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| In: |
Constructive approximation
Year: 2016, Volume: 47, Issue: 1, Pages: 39-74 |
| ISSN: | 1432-0940 |
| DOI: | 10.1007/s00365-016-9357-z |
| Online Access: | Verlag, Volltext: https://doi.org/10.1007/s00365-016-9357-z
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| Author Notes: | Laurent Bétermin, Etienne Sandier |
| Summary: | 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. |
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| Item Description: | Gesehen am 14.08.2019 Published online: 15 September 2016 |
| Physical Description: | Online Resource |
| ISSN: | 1432-0940 |
| DOI: | 10.1007/s00365-016-9357-z |