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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…