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 |
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| 520 | |a 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. | ||
| 534 | |c 2016 | ||
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| 650 | 4 | |a Coulomb gas | |
| 650 | 4 | |a Crystallization | |
| 650 | 4 | |a Gamma-convergence | |
| 650 | 4 | |a Ginzburg–Landau | |
| 650 | 4 | |a Logarithmic energy | |
| 650 | 4 | |a Logarithmic potential theory | |
| 650 | 4 | |a Number theory | |
| 650 | 4 | |a Primary 52A40 | |
| 650 | 4 | |a Renormalized energy | |
| 650 | 4 | |a Secondary 41A60 | |
| 650 | 4 | |a Triangular lattice | |
| 650 | 4 | |a Vortices | |
| 650 | 4 | |a Weak confinement | |
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