Title:	Extreme statistics and index distribution in the classical 1d Coulomb gas
Authors:	Dhar, Abhishek Kundu, Anupam Majumdar, Satya N. Sabhapandit, Sanjib Schehr, Grégory
Issue Date:	12-Jun-2018
Publisher:	IOP Publishing Ltd
Citation:	Journal of Physics A: Mathematical and Theoretical, 2018, Vol.51, p295001
Abstract:	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 an average, uniformly and symmetrically on a finite region centred around the origin. We study the statistics of the position of the rightmost particle and show that the limiting distribution describing its typical fluctuations is different from the Tracy–Widom distribution found in the 1D log-gas. We also compute the large deviation functions which characterise the atypical fluctuations of far away from its mean value. In addition, we study the gap between the two rightmost particles as well as the index N + , i.e. the number of particles on the positive semi-axis. We compute the limiting distributions associated to the typical fluctuations of these observables as well as the corresponding large deviation functions. We provide numerical supports to our analytical predictions. Part of these results were announced in a recent letter, Dhar et al (2017 Phys. Rev. Lett. 119 060601).
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/6952
ISSN:	0305-4470. 1361-6447(Online)
Alternative Location:	https://arxiv.org/abs/1802.10374 DOI: 10.1088/1751-8121/aac75f
Copyright:	2018 IOP Publishing Ltd
Appears in Collections:	Research Papers (A&A)

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