TY - JOUR

T1 - The two-dimensional Coulomb plasma

T2 - Quasi-free approximation and central limit theorem

AU - Bauerschmidt, Roland

AU - Bourgadey, Paul

AU - Nikula, Miika

AU - Yauz, Horng Tzer

N1 - Funding Information:
†Partially supported by NSF grant DMS-1513587. ‡Partially supported by NSF grant DMS-1606305, 1855509 and a Simons Investigator award.
Publisher Copyright:
© International Press of Boston, Inc.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

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U2 - 10.4310/ATMP.2019.v23.n4.a1

DO - 10.4310/ATMP.2019.v23.n4.a1

M3 - Article

AN - SCOPUS:85079388400

SN - 1095-0761

VL - 23

SP - 841

EP - 1002

JO - Advances in Theoretical and Mathematical Physics

JF - Advances in Theoretical and Mathematical Physics

IS - 4

ER -