At the edge of a one-dimensional jellium

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We consider a one-dimensional classical Wigner jellium, not necessarily charge neutral, for which the electrons are allowed to exist beyond the support of the background charge. The model can be seen as a one-dimensional Coulomb gas in which the external field is generated by a smeared background on an interval. It is a true one-dimensional Coulomb gas and not a one-dimensional log-gas. The system exists if and only if the total background charge is greater than the number of electrons minus one. For various backgrounds, we show convergence to point processes, at the edge of the support of the background. In particular, this provides asymptotic analysis of the fluctuations of the right-most particle. Our analysis reveals that these fluctuations are not universal, in the sense that depending on the background, the tails range anywhere from exponential to Gaussian-like behavior, including for instance Tracy-Widom-like behavior. We also obtain a Renyi-type probabilistic representation for the order statistics of the particle system beyond the support of the background.
Publisher
INT STATISTICAL INST
Issue Date
2022-08
Language
English
Article Type
Article
Citation

BERNOULLI, v.28, no.3, pp.1784 - 1809

ISSN
1350-7265
DOI
10.3150/21-BEJ1397
URI
http://hdl.handle.net/10203/296635
Appears in Collection
MA-Journal Papers(저널논문)
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