The two-dimensional Coulomb plasma: Quasi-free approximation and central limit theorem

Roland Bauerschmidt, Paul Bourgadey, Miika Nikula, Horng Tzer Yauz

Research output: Contribution to journalArticlepeer-review

Abstract

For the two-dimensional one-component Coulomb plasma, we derive an asymptotic expansion of the free energy up to order N, the number of particles of the gas, with an effective error bound N1-κ for some constant κ > 0. This expansion is based on approximating the Coulomb gas by a quasi-free Yukawa gas. Further, we prove that the fluctuations of the linear statistics are given by a Gaussian free field at any positive temperature. Our proof of this central limit theorem uses a loop equation for the Coulomb gas, the free energy asymptotics, and rigidity bounds on the local density fluctuations of the Coulomb gas, which we obtained in a previous paper.

Original languageEnglish (US)
Pages (from-to)841-1002
Number of pages162
JournalAdvances in Theoretical and Mathematical Physics
Volume23
Issue number4
DOIs
StatePublished - 2019

ASJC Scopus subject areas

  • General Mathematics
  • General Physics and Astronomy

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