Title:	Exact extremal statistics in the classical 1D coulomb gas.
Authors:	Dhar, Abhishek Kundu, Anupam Majumdar, Satya N. Sabhapandit, Sanjib Schehr, Gregory
Issue Date:	Aug-2017
Publisher:	American Physical Society
Citation:	Physical Review Letters, 2017, Vol. 119, p 060601
Abstract:	We consider a one-dimensional classical Coulomb gas of N-like charges in a harmonic potential—also known as the one-dimensional one-component plasma. We compute, analytically, the probability distribution of the position xmax of the rightmost charge in the limit of large N. We show that the typical fluctuations of xmax around its mean are described by a nontrivial scaling function, with asymmetric tails. This distribution is different from the Tracy-Widom distribution of xmax for Dyson’s log gas. We also compute the large deviation functions of xmax explicitly and show that the system exhibits a third-order phase transition, as in the log gas. Our theoretical predictions are verified numerically.
Description:	Open Access
URI:	http://hdl.handle.net/2289/6796
ISSN:	0031-9007 1079-7114(Online)
Alternative Location:	http://arxiv.org/abs/1704.08973 http://dx.doi.org/10.1103/PhysRevLett.119.060601
Copyright:	2017 American Physical Society
Appears in Collections:	Research Papers (TP)

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