Universal behavior of the full particle statistics of one-dimensional Coulomb gases with an arbitrary external potential

Abstract

We present a complete theory for the full particle statistics of the positions of bulk and extremal particles in a one-dimensional Coulomb Gas (CG) with an arbitrary potential, in the typical and large deviations regimes. Typical fluctuations are described by a universal function which depends solely on general properties of the external potential. The rate function controlling large deviations is, rather unexpectedly, not strictly convex and has a discontinuous third derivative around its minimum for both extremal and bulk particles. This implies, in turn, that the rate function cannot predict the anomalous scaling of the typical fluctuations with the system size. Moreover, its asymptotic behavior for extremal particles differs from the predictions of the Tracy-Widom distribution. Thus many of the paradigmatic properties of the full particle statistics of two-dimensional systems do \emph{not} carry out into their one-dimensional counterparts, hence proving that 1d CG belongs to a different universality class. Our analytical expressions are thoroughly compared with Monte Carlo simulations showing excellent agreement.

arXiv comment5 pages, 6 figures. SI as ancillary file

References in corpus (30)

• The large deviation approach to statistical mechanics
• Level-Spacing Distributions and the Airy Kernel
• Electrostatic correlations: from Plasma to Biology
• On Orthogonal and Symplectic Matrix Ensembles
• One-Dimensional Hole Gas in Germanium/Silicon Nanowire Heterostructures
• Large Deviations of Extreme Eigenvalues of Random Matrices
• Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices
• Top eigenvalue of a random matrix: large deviations and third order phase transition
• Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices
• Gaussian fluctuations of eigenvalues in the GUE
• Large Deviations of the Maximum Eigenvalue in Wishart Random Matrices
• A minimal model of dynamical phase transition
• The Index Distribution of Gaussian Random Matrices
• First order global asymptotics for confined particles with singular pair repulsion
• How many eigenvalues of a Gaussian random matrix are positive?
• Exact extremal statistics in the classical $1d$ Coulomb gas
• Gaussian Fluctuations of Eigenvalues in Wigner Random Matrices
• Large Deviations of the Smallest Eigenvalue of the Wishart-Laguerre Ensemble
• Extremes of $2d$ Coulomb gas: universal intermediate deviation regime
• Invariant $\beta$-Wishart ensembles, crossover densities and asymptotic corrections to the Marchenko-Pastur law
• Universality of the third-order phase transition in the constrained Coulomb gas
• Large deviation function for the number of eigenvalues of sparse random graphs inside an interval
• Spectral order statistics of Gaussian random matrices: large deviations for trapped fermions and associated phase transitions
• The effects of dielectric disorder on van der Waals interactions in slab geometries
• Screening like-charges in one-dimensional Coulomb systems: Exact results
• Large deviations of the top eigenvalue of large Cauchy random matrices
• Large deviation theory for diluted Wishart random matrices
• Spectral Properties of the Jacobi Ensembles via the Coulomb Gas approach
• Phase transitions in the condition number distribution of Gaussian random matrices
• A unified approach for large deviations of bulk and extreme eigenvalues of the Wishart ensemble

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