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Pré-Publication, Document De Travail Année : 2020

A Uniqueness Result for Minimizers of the 1D Log-gas Renormalized Energy

Thomas Leblé

Résumé

In [SS13] Sandier and Serfaty studied the one-dimensional Log-gas model, in particular they gave a crystallization result by showing that the one-dimensional lattice Z is a minimizer for the so-called renormalized energy which they obtained as a limit of the Nparticle Log-gas Hamiltonian for N → ∞. However, this minimizer is not unique among infinite point configurations (for example local perturbations of Z leave the renormalized energy unchanged). In this paper, we establish that uniqueness holds at the level of (stationary) point processes, the only minimizer being given by averaging Z over a choice of the origin in [0, 1]. This is proved by showing a quantitative estimate on the two-point correlation function of a process in terms of its renormalized energy.
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hal-03040302 , version 1 (04-12-2020)

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  • HAL Id : hal-03040302 , version 1

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Thomas Leblé. A Uniqueness Result for Minimizers of the 1D Log-gas Renormalized Energy. 2020. ⟨hal-03040302⟩
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