40 citations · 223 across the 39 of their papers we have counts for
46 papers
Random normal matrices: eigenvalue correlations near a hard wall
Yacin Ameur, Christophe Charlier, Joakim Cronvall
We study pair correlation functions for planar Coulomb systems in the pushed phase, near a ring-shaped impenetrable wall. We assume coupling constant and that the number …
Eigenvalues of truncated unitary matrices: disk counting statistics
Yacin Ameur, Christophe Charlier, Philippe Moreillon
Let be an truncation of an Haar distributed unitary matrix. We consider the disk counting statistics of the eigenvalues of . We prove that as…
Boussinesq's equation for water waves: asymptotics in Sector I
Christophe Charlier, Jonatan Lenells
In a recent paper, we showed that the large behavior of a class of physically relevant solutions of Boussinesq's equation for water waves is described by ten main asymptoti…
The soliton resolution conjecture for the Boussinesq equation
Christophe Charlier, Jonatan Lenells
We analyze the Boussinesq equation on the line with Schwartz initial data belonging to the physically relevant class of global solutions. In a recent paper, we determined ten main…
Boussinesq's equation for water waves: the soliton resolution conjecture for Sector IV
Christophe Charlier, Jonatan Lenells
We consider the Boussinesq equation on the line for a broad class of Schwartz initial data relevant for water waves. In a recent work, we identified ten main sectors describing the…
Direct and inverse scattering for the Boussinesq equation with solitons
Christophe Charlier, Jonatan Lenells
In a recent paper, we developed an inverse scattering approach to the Boussinesq equation in the case when no solitons are present. In this paper, we extend this approach to includ…
Boussinesq's equation for water waves: asymptotics in sector V
Christophe Charlier, Jonatan Lenells
We consider the Boussinesq equation on the line for a broad class of Schwartz initial data for which (i) no solitons are present, (ii) the spectral functions have generic behavior…
Miura transformation for the "good'' Boussinesq equation
Christophe Charlier, Jonatan Lenells
It is well-known that each solution of the mKdV equation gives rise, via the Miura transformation, to a solution of the KdV equation. In this work, we show that a similar Miura-typ…
A point process on the unit circle with antipodal interactions
Christophe Charlier
We introduce the point process \begin{align*} \frac{1}{Z_{n}}\prod_{1 \leq j < k \leq n} |e^{iθ_{j}}+e^{iθ_{k}}|^β\prod_{j=1}^{n} dθ_{j}, \qquad θ_{1},\ldots,θ_{n} \in (-π,π], \qua…
A point process on the unit circle with mirror-type interactions
Christophe Charlier
We consider the point process \begin{align*} \frac{1}{Z_{n}}\prod_{1 \leq j < k \leq n} |e^{iθ_{j}}-e^{-iθ_{k}}|^β\prod_{j=1}^{n} dθ_{j}, \qquad θ_{1},\ldots,θ_{n} \in (-π,π], \qua…
Toeplitz determinants with a one-cut regular potential and Fisher--Hartwig singularities I. Equilibrium measure supported on the unit circle
Elliot Blackstone, Christophe Charlier, Jonatan Lenells
We consider Toeplitz determinants whose symbol has: (i) a one-cut regular potential , (ii) Fisher--Hartwig singularities, and (iii) a smooth function in the background. The pote…
Disk counting statistics near hard edges of random normal matrices: the multi-component regime
Yacin Ameur, Christophe Charlier, Joakim Cronvall +1
We consider a two-dimensional point process whose points are separated into two disjoint components by a hard wall, and study the multivariate moment generating function of the cor…
The two-dimensional Coulomb gas: fluctuations through a spectral gap
Yacin Ameur, Christophe Charlier, Joakim Cronvall
We study a class of radially symmetric Coulomb gas ensembles at inverse temperature , for which the droplet consists of a number of concentric annuli, having at least one boun…
Exponential moments for disk counting statistics at the hard edge of random normal matrices
Yacin Ameur, Christophe Charlier, Joakim Cronvall +1
We consider the multivariate moment generating function of the disk counting statistics of a model Mittag-Leffler ensemble in the presence of a hard wall. Let be the number of…
On the almost-circular symplectic induced Ginibre ensemble
Sung-Soo Byun, Christophe Charlier
We consider the symplectic induced Ginibre process, which is a Pfaffian point process on the plane. Let be the number of points. We focus on the almost-circular regime where mo…
On the characteristic polynomial of the eigenvalue moduli of random normal matrices
Sung-Soo Byun, Christophe Charlier
We study the characteristic polynomial where the are drawn from the Mittag-Leffler ensemble, i.e. a two-dimensional determinantal poin…
Exponential moments for disk counting statistics of random normal matrices in the critical regime
Christophe Charlier, Jonatan Lenells
We obtain large asymptotics for the -point moment generating function of the disk counting statistics of the Mittag-Leffler ensemble. We focus on the critical regime where a…
Uniform tail asymptotics for Airy kernel determinant solutions to KdV and for the narrow wedge solution to KPZ
Christophe Charlier, Tom Claeys, Giulio Ruzza
We obtain uniform asymptotics for deformed Airy kernel determinants, which arise in models of finite temperature free fermions and which characterize the narrow wedge solution of t…
Large gap asymptotics on annuli in the random normal matrix model
Christophe Charlier
We consider a two-dimensional determinantal point process arising in the random normal matrix model and which is a two-parameter generalization of the complex Ginibre point process…
Asymptotics of determinants with a rotation-invariant weight and discontinuities along circles
Christophe Charlier
We study the moment generating function of the disk counting statistics of a two-dimensional determinantal point process which generalizes the complex Ginibre point process. This m…
On the generating function of the Pearcey process
Christophe Charlier, Philippe Moreillon
The Pearcey process is a universal point process in random matrix theory. In this paper, we study the generating function of the Pearcey process on any number of intervals. We…
The hard-to-soft edge transition: exponential moments, central limit theorems and rigidity
Christophe Charlier, Jonatan Lenells
The local eigenvalue statistics of large random matrices near a hard edge transitioning into a soft edge are described by the Bessel process associated with a large parameter .…
Asymptotics of Muttalib-Borodin determinants with Fisher-Hartwig singularities
Christophe Charlier
Muttalib-Borodin determinants are generalizations of Hankel determinants and depend on a parameter . In this paper, we obtain large asymptotics for Muttalib-B…
Long-time asymptotics for an integrable evolution equation with a Lax pair
Christophe Charlier, Jonatan Lenells
We derive a Riemann--Hilbert representation for the solution of an integrable nonlinear evolution equation with a Lax pair. We use the derived representation to obtain…