7 papers
Hole probabilities and balayage of measures for planar Coulomb gases
Christophe Charlier
We study hole probabilities of two-dimensional Coulomb gases with a general potential and arbitrary temperature. The hole region is assumed to satisfy , wh…
Blow-up solutions of the "bad" Boussinesq equation
Christophe Charlier
We study blow-up solutions of the ``bad" Boussinesq equation, and prove that a wide range of asymptotic scenarios can happen. For example, for each , and…
The "good" Boussinesq equation on the half-line: a Riemann-Hilbert approach
Christophe Charlier, Jonatan Lenells
We consider the ``good" Boussinesq equation on the half-line. Assuming existence of the solution, we prove that it can be recovered from the solution of a Riemann-Hilbe…
Balayage of measures: behavior near a corner
Christophe Charlier, Jonatan Lenells
We consider the balayage of a measure defined on a domain onto its boundary . Assuming that has a corner of opening at a point $z_0 \in \partial…
On the Hartree-Fock phase diagram for the two-dimensional Hubbard model
Christophe Charlier, Edwin Langmann, Jonatan Lenells
We propose an analytical method for the construction of Hartree-Fock phase diagrams for the (fermion) Hubbard model and various generalizations thereof. Such phase diagrams are tra…
Free energy and fluctuations in the random normal matrix model with spectral gaps
Yacin Ameur, Christophe Charlier, Joakim Cronvall
We study large expansions for the partition function of a Coulomb gas $$Z_n=\frac 1 {Ï^n}\int_{\mathbb{C}^n}\prod_{1\le i<j\le n}|z_i-z_j|^2\prod_{i=1}^n e^{-nQ(z_i)}\, d^2 z_…