Energy of the Coulomb Gas on the Sphere at Low Temperature
We consider the Coulomb gas of N particles on the sphere and show that the logarithmic energy of the configurations approaches the minimal energy up to an error of order log N, with exponentially high probability and on average, provided the temperature is O ( 1 / N ) .
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| Veröffentlicht in: | Archive for rational mechanics and analysis 2019-03, Vol.231 (3), p.2007-2017 |
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| container_end_page | 2017 |
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| container_issue | 3 |
| container_start_page | 2007 |
| container_title | Archive for rational mechanics and analysis |
| container_volume | 231 |
| creator | Beltrán, Carlos Hardy, Adrien |
| description | We consider the Coulomb gas of
N
particles on the sphere and show that the logarithmic energy of the configurations approaches the minimal energy up to an error of order log
N,
with exponentially high probability and on average, provided the temperature is
O
(
1
/
N
)
. |
| doi_str_mv | 10.1007/s00205-018-1316-3 |
| format | Article |
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N
particles on the sphere and show that the logarithmic energy of the configurations approaches the minimal energy up to an error of order log
N,
with exponentially high probability and on average, provided the temperature is
O
(
1
/
N
)
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N
particles on the sphere and show that the logarithmic energy of the configurations approaches the minimal energy up to an error of order log
N,
with exponentially high probability and on average, provided the temperature is
O
(
1
/
N
)
.</description><subject>Classical Analysis and ODEs</subject><subject>Classical Mechanics</subject><subject>Complex Systems</subject><subject>Fluid- and Aerodynamics</subject><subject>Low temperature</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Physics</subject><subject>Mathematics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Probability</subject><subject>Theoretical</subject><issn>0003-9527</issn><issn>1432-0673</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kM1OwzAQhC0EEqXwANwsceJg2LUTO-ZWVaVFisSBcrbc4PRHbRzsBNS3JyEITpxWO_pmtDuEXCPcIYC6jwAcUgaYMRQomTghI0wEZyCVOCUjABBMp1ydk4sYd_3KhRyRh1nlwvpIfUmbjaNT3-79YUXnNlJffUsv9cYFR21Dc_9Jl-5Qu2CbNrhLclbafXRXP3NMXh9ny-mC5c_zp-kkZ4VIoWEKUUKm5BuWSgkEJa1alYnVDjEVq8Jqm2SixCwDV0qHnBdpAcJhIYTWnIsxuR1yN3Zv6rA92HA03m7NYpKbXuue1oA8_cCOvRnYOvj31sXG7Hwbqu48w1Fq0XWU6I7CgSqCjzG48jcWwfR1mqHOPtn0dRrRefjgiR1brV34S_7f9AWXlnNp</recordid><startdate>20190307</startdate><enddate>20190307</enddate><creator>Beltrán, Carlos</creator><creator>Hardy, Adrien</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0001-7452-2838</orcidid></search><sort><creationdate>20190307</creationdate><title>Energy of the Coulomb Gas on the Sphere at Low Temperature</title><author>Beltrán, Carlos ; Hardy, Adrien</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c350t-71160876d1f7731076a7bf4a9e1153bca9a483f1880ef6e122c5c03e1c3399223</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Classical Analysis and ODEs</topic><topic>Classical Mechanics</topic><topic>Complex Systems</topic><topic>Fluid- and Aerodynamics</topic><topic>Low temperature</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Physics</topic><topic>Mathematics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Probability</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Beltrán, Carlos</creatorcontrib><creatorcontrib>Hardy, Adrien</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Archive for rational mechanics and analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Beltrán, Carlos</au><au>Hardy, Adrien</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Energy of the Coulomb Gas on the Sphere at Low Temperature</atitle><jtitle>Archive for rational mechanics and analysis</jtitle><stitle>Arch Rational Mech Anal</stitle><date>2019-03-07</date><risdate>2019</risdate><volume>231</volume><issue>3</issue><spage>2007</spage><epage>2017</epage><pages>2007-2017</pages><issn>0003-9527</issn><eissn>1432-0673</eissn><abstract>We consider the Coulomb gas of
N
particles on the sphere and show that the logarithmic energy of the configurations approaches the minimal energy up to an error of order log
N,
with exponentially high probability and on average, provided the temperature is
O
(
1
/
N
)
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| ispartof | Archive for rational mechanics and analysis, 2019-03, Vol.231 (3), p.2007-2017 |
| issn | 0003-9527 1432-0673 |
| language | eng |
| recordid | cdi_hal_primary_oai_HAL_hal_01890125v1 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Classical Analysis and ODEs Classical Mechanics Complex Systems Fluid- and Aerodynamics Low temperature Mathematical and Computational Physics Mathematical Physics Mathematics Physics Physics and Astronomy Probability Theoretical |
| title | Energy of the Coulomb Gas on the Sphere at Low Temperature |
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