# 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…

## 7 Citations

Gap probability and full counting statistics in the one-dimensional one-component plasma

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2022

We consider the 1d one-component plasma in thermal equilibrium, consisting of N equally charged particles on a line, with pairwise Coulomb repulsion and confined by an external harmonic potential. We…

Edge fluctuations and third-order phase transition in harmonically confined long-range systems

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2022

We study the distribution of the position of the rightmost particle x max in a N-particle Riesz gas in one dimension confined in a harmonic trap. The particles interact via long-range repulsive…

General truncated linear statistics for the top eigenvalues of random matrices

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2022

Invariant ensembles, which are characterised by the joint distribution of eigenvalues P(λ 1, …, λ N ), play a central role in random matrix theory. We consider the truncated linear statistics…

Ranked diffusion, delta Bose gas, and Burgers equation

- Physics, MathematicsPhysical Review E
- 2022

We study the diffusion of N particles in one dimension interacting via a drift proportional to their rank. In the attractive case (self-gravitating gas) a mapping to the Lieb-Liniger quantum model…

Ranked diffusion, delta Bose gas and Burgers equation

- Physics, Mathematics
- 2021

We study the diffusion of N particles in one dimension interacting via a drift proportional to their rank. In the attractive case (self-gravitating gas) a mapping to the Lieb Liniger quantum model…

Stability of large complex systems with heterogeneous relaxation dynamics

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2021

We study the probability of stability of a large complex system of size N within the framework of a generalized May model, which assumes a linear dynamics of each population size n i (with respect to…

Coulomb and Riesz gases: The known and the unknown

- MathematicsJournal of Mathematical Physics
- 2022

We review what is known, unknown, and expected about the mathematical properties of Coulomb and Riesz gases. Those describe infinite configurations of points in [Formula: see text] interacting with…

## References

SHOWING 1-10 OF 41 REFERENCES

Extreme statistics and index distribution in the classical 1d Coulomb gas

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2018

We consider a 1D gas of N charged particles confined by an external harmonic potential and interacting via the 1D Coulomb potential. For this system we show that in equilibrium the charges settle, on…

Exact Extremal Statistics in the Classical 1D Coulomb Gas.

- PhysicsPhysical review letters
- 2017

The probability distribution of the position x_{max} of the rightmost charge in the limit of large N is computed and it is shown that the typical fluctuations of x_{ max} around its mean are described by a nontrivial scaling function, with asymmetric tails.

Harmonically Confined Particles with Long-Range Repulsive Interactions.

- MathematicsPhysical review letters
- 2019

The average density profile for large N for all k>-2 is computed and it is shown that while it is independent of temperature for sufficiently low temperature, it has a rich and nontrivial dependence on k with distinct behavior for -21 and k=1.

Current fluctuations in noninteracting run-and-tumble particles in one dimension.

- Physics, MathematicsPhysical review. E
- 2020

We present a general framework to study the distribution of the flux through the origin up to time t, in a noninteracting one-dimensional system of particles with a step initial condition with a…

Top eigenvalue of a random matrix: large deviations and third order phase transition

- Physics
- 2014

We study the fluctuations of the largest eigenvalue λmax of N × N random matrices in the limit of large N. The main focus is on Gaussian β ensembles, including in particular the Gaussian orthogonal…

Distribution of spectral linear statistics on random matrices beyond the large deviation function—Wigner time delay in multichannel disordered wires

- Mathematics
- 2016

An invariant ensemble of N × N random matrices can be characterised by a joint distribution for eigenvalues P ( λ 1 , ⋯ , λ N ) . The distribution of linear statistics, i.e. of quantities of the form…

Ground-state energy of noninteracting fermions with a random energy spectrum

- PhysicsEPL (Europhysics Letters)
- 2018

We derive analytically the full distribution of the ground-state energy of K non-interacting fermions in a disordered environment, modelled by a Hamiltonian whose spectrum consists of N i.i.d. random…

One-Dimensional Coulomb Systems

- Physics
- 1981

The basic role played by Coulomb interactions in physics makes them of interest even in one dimension. This explains the effort devoted over the last years to the elucidation of physical properties…

Condensation transition in the late-time position of a run-and-tumble particle.

- MathematicsPhysical review. E
- 2021

The position distribution of a run-and-tumble particle (RTP) in arbitrary dimension d, after N runs is studied and it is shown that, under certain conditions on d and W(v) and for large N, a condensation transition occurs at some critical value of R=R_{c}∼O(N) located in the large-deviation regime of P(R,N).

High-precision simulation of the height distribution for the KPZ equation

- Physics
- 2018

The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high…