相关论文: Partition function for the 2d Coulomb gas on a Jor…

We study a planar Coulomb gas confined to a sufficiently smooth Jordan arc $\gamma$ in the complex plane, at inverse temperature $\beta > 0$. Let \[\bar{Z}_{n}^\beta(\gamma) = Z_{n}^\beta(\gamma)/\left(2 \textrm{cap}(\gamma)\right)^{\beta…

The large $N$ asymptotic expansion of the partition function for the normal matrix model is predicted to have special features inherited from its interpretation as a two-dimensional Coulomb gas. However for the latter, it is most natural to…

We study a two-dimensional Coulomb gas consisting of a mixture of particles carrying various positive multiple integer charges, confined on a unit circle. We consider the system in the canonical and grand canonical ensembles, and attempt to…

We consider certain determinants with respect to a sufficiently regular Jordan curve $\gamma$ in the complex plane that generalize Toeplitz determinants which are obtained when the curve is the circle. This also corresponds to studying a…

Two-dimensional Coulomb gases on an annulus at a special inverse temperature $\beta = 2$ are studied by using the orthogonal polynomial method borrowed from the theory of random matrices. The correlation functions among the Coulomb gas…

Let $D$ be a Jordan domain of unit capacity. We study the partition function of a planar Coulomb gas in $D$ with a hard wall along $\eta = \partial D$, \[Z_{n}(D) =\frac 1{n!}\int_{D^n}\prod_{1\le k < \ell \le n}|z_k-z_\ell|^{2}…

We prove a Central Limit Theorem for the linear statistics of two-dimensional Coulomb gases, with arbitrary inverse temperature and general confining potential, at the macroscopic and mesoscopic scales and possibly near the boundary of the…

It is well-known that two-dimensional Coulomb gases at a special inverse temperature $\beta = 2$ can be analyzed by using the orthogonal polynomial method borrowed from the theory of random matrices. In this paper, such Coulomb gas…

The statistical mechanics of a two dimensional Coulomb gas confined to one dimension is studied, wherein hard core particles move on a ring. Exact self-duality is shown for a version of the sine-Gordon model arising in this context, thereby…

We study a class of radially symmetric Coulomb gas ensembles at inverse temperature $\beta=2$, for which the droplet consists of a number of concentric annuli, having at least one bounded ``gap'' $G$, i.e., a connected component of the…

We construct a probability model seemingly unrelated to the considered stochastic process of coagulation and fragmentation. By proving for this model the local limit theorem, we establish the asymptotic formula for the partition function of…

Zabrodin recently proposed a generalization of Dyson Brownian motion to a setting where the particles are confined to a smooth Jordan curve in the plane. In this paper, we discuss a rigorous construction of such a process on a rectifiable…

For the two-dimensional one-component Coulomb plasma, we derive an asymptotic expansion of the free energy up to order $N$, the number of particles of the gas, with an effective error bound $N^{1-\kappa}$ for some constant $\kappa > 0$.…

We consider a two-dimensional bi-layered loop model with a certain interlayer coupling and study its spectrum on a torus. Each layer consists of an $O(n)$ model on a honeycomb lattice with periodic boundary conditions; these layers are…

We investigate a family of radially symmetric Coulomb gas systems at inverse temperature $\beta = 2$. The family is characterised by the property that the density of the equilibrium measure vanishes on a ring at radius $r_*$, which lies…

The model under consideration is an asymmetric two-dimensional Coulomb gas of positively (q_1=+1) and negatively (q_2=-1/2) charged pointlike particles, interacting via a logarithmic potential. This continuous system is stable against…

We study the non-asymptotic behavior of a Coulomb gas on a compact Riemannian manifold. This gas is a symmetric n-particle Gibbs measure associated to the two-body interaction energy given by the Green function. We encode such a particle…

We consider a class of external potentials on the complex plane $\mathbb{C}$ for which the coincidence set to the obstacle problem contains a Jordan curve in the exterior of the droplet. We refer to this curve as a spectral outpost. We…

We investigate a one-parameter family of Coulomb gases in two dimensions, which are confined to an ellipse, due to a hard wall constraint, and are subject to an additional external potential. At inverse temperature $\beta=2$ we can use the…

This article extends recent results on log-Coulomb gases in a $p$-field $K$ (i.e., a nonarchimedean local field) to those in its projective line $\mathbb{P}^1(K)$, where the latter is endowed with the $PGL_2$-invariant Borel probability…