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Gradient flow of the infinite-volume free energy for lattice systems of continuous spins
Ronan Herry, Thomas Leblé
We consider an infinite lattice system of interacting spins living on a smooth compact manifold, with short- but not necessarily finite-range pairwise interactions. We construct th…
DLR equations, number-rigidity and translation-invariance for infinite-volume limit points of the 2DOCP
Thomas Leblé
We prove that, at arbitrary positive temperature, every infinite-volume local limit point of the two-dimensional one-component plasma (2DOCP, also known as Coulomb or log-gas, or j…
(Non)-hyperuniformity of perturbed lattices
David Dereudre, Daniela Flimmel, Martin Huesmann +1
We ask whether a stationary lattice in dimension whose points are shifted by identically distributed but possibly dependent perturbations remains hyperuniform. When or…
The link between hyperuniformity, Coulomb energy, and Wasserstein distance to Lebesgue for two-dimensional point processes
Martin Huesmann, Thomas Leblé
We investigate the interplay between three possible properties of stationary point processes: i) Finite Coulomb energy with short-scale regularization, ii) Finite -Wasserstein t…
Law of large numbers for the maximum of the two-dimensional Coulomb gas potential
Gaultier Lambert, Thomas Leblé, Ofer Zeitouni
We derive the leading order asymptotics of the logarithmic potential of a two dimensional Coulomb gas at arbitrary positive temperature. The proof is based on precise evaluation of…