Coulomb Gases Under Constraint: Some Theoretical and Numerical Results
نویسندگان
چکیده
We consider Coulomb gas models for which the empirical measure typically concentrates, when number of particles becomes large, on an equilibrium minimizing electrostatic energy. study behavior is conditioned a rare event. first show that special case quadratic confinement and linear constraint exactly solvable due to remarkable factorization, conditioning has then simple effect shifting cloud without deformation. To address more general cases, we perform theoretical asymptotic analysis relying large deviations technique known as Gibbs principle. The technical part amounts establishing ensemble I-continuity set This leads characterizing solution modified variational problem. For simplicity, focus statistics constraints. Finally, numerically illustrate our predictions explore cases in no explicit known. this, use Generalized Hybrid Monte Carlo algorithm sampling from distribution finite but system.
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ژورنال
عنوان ژورنال: Siam Journal on Mathematical Analysis
سال: 2021
ISSN: ['0036-1410', '1095-7154']
DOI: https://doi.org/10.1137/19m1296859