Local Density for Two-Dimensional One-Component Plasma

Roland Bauerschmidt, Paul Bourgade, Miika Nikula, Horng Tzer Yau

Research output: Contribution to journalArticle

Abstract

We study the classical two-dimensional one-component plasma of N positively charged point particles, interacting via the Coulomb potential and confined by an external potential. For the specific inverse temperature β= 1 (in our normalization), the charges are the eigenvalues of random normal matrices, and the model is exactly solvable as a determinantal point process. For any positive temperature, using a multiscale scheme of iterated mean-field bounds, we prove that the equilibrium measure provides the local particle density down to the optimal scale of No ( 1 ) particles. Using this result and the loop equation, we further prove that the particle configurations are rigid, in the sense that the fluctuations of smooth linear statistics on any scale are No ( 1 ).

Original languageEnglish (US)
Pages (from-to)189-230
Number of pages42
JournalCommunications In Mathematical Physics
Volume356
Issue number1
DOIs
StatePublished - Nov 1 2017

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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