Truncated linear statistics in the one dimensional one-component plasma

@article{Flack2021TruncatedLS,
  title={Truncated linear statistics in the one dimensional one-component plasma},
  author={Ana Flack and Satya N. Majumdar and Gr{\'e}gory Schehr},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2021},
  volume={54}
}
In this paper, we study the probability distribution of the observable s=(1/N)∑i=N−N′+1Nxi , with 1 ⩽ N′ ⩽ N and x 1 < x 2 <⋯< x N representing the ordered positions of N particles in a 1D one-component plasma, i.e. N harmonically confined charges on a line, with pairwise repulsive 1D Coulomb interaction |x i − x j |. This observable represents an example of a truncated linear statistics—here proportional to the center of mass of the N′ = κN (with 0 < κ ⩽ 1), rightmost particles. It… 
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