English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present a complete theory for the full particle statistics of thepositions 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 solelyon general properties of the external potential. The rate function controllinglarge deviations is, rather unexpectedly, not strictly convex and has adiscontinuous third derivative around its minimum for both extremal and bulkparticles. This implies, in turn, that the rate function cannot predict theanomalous scaling of the typical fluctuations with the system size. Moreover,its asymptotic behavior for extremal particles differs from the predictions ofthe Tracy-Widom distribution. Thus many of the paradigmatic properties of thefull particle statistics of two-dimensional systems do \emph{not} carry outinto their one-dimensional counterparts, hence proving that 1d CG belongs to adifferent universality class. Our analytical expressions are thoroughlycompared with Monte Carlo simulations showing excellent agreement.

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