Related papers: The polyanalytic Ginibre ensembles
We consider a Bose-Einstein condensate in a 2D dilute Bose gas, with an external potential and an interaction potential containing both of the short-range attractive self-interaction and the long-range self-gravitating effect. We prove the…
We consider a functional related with phase transition models in the Heisenberg group framework. We prove that level sets of local minimizers satisfy some density estimates, that is, they behave as "codimension one" sets. We thus deduce a…
In several fields of Physics, Chemistry and Ecology, some models are described by Liouville systems. In this article we first prove a uniqueness result for a Liouville system in $\mathbb R^2$. Then we establish an uniform estimate for…
For an additive perturbation of the complex Ginibre ensemble under a deterministic matrix $X_0$, under certain assumption on $X_0$, we observe that there are only two kinds of local statistical patterns at the spectral edge: GinUE…
We study the deformed complex Ginibre ensemble $H=A_0+H_0$, where $H_0$ is the complex matrix with iid Gaussian entries, and $A_0$ is some general $n\times n$ matrix (it can be random and in this case it is independent of $H_0$). Assuming…
The present paper is a continuation of [5], where Lie bialgebra structures on g[u] were studied. These structures fall into different classes labelled by the vertices of the extended Dynkin diagram of g. In [5] the Lie bialgebras…
In this paper we study the limiting distribution of the $k$ smallest gaps between eigenvalues of three kinds of random matrices -- the Ginibre ensemble, the Wishart ensemble and the universal unitary ensemble. All of them follow a…
We establish large deviation principles for the extremal eigenvalues of the Ginibre ensembles with good rate functions. In contrast to the typical estimates for the extremal eigenvalues, the large deviations for the real Ginibre ensemble…
We consider the energy of a randomly charged polymer. We assume that only charges on the same site interact pairwise. We study the lower tails of the energy, when averaged over both randomness, in dimension three or more. As a corollary, we…
The aim of this note is to investigate the relation between two types of non-singular projective varieties of Picard rank 2, namely the Projective bundles over Projective spaces and certain Blow-up of Projective spaces.
The effect of polydispersity on the phase diagram of a simple binary mixture is to split the binodal curve into cloud and shadow curves that cross at the critical point (which, in general, is not at the maximum of either curve). Recent…
We have mapped the physics of polymer melts onto a time-dependent Landau-Ginzburg $|\psi|^4$ field theory using techniques of functional integration. Time in the theory is simply a label for the location of a given monomer along the extent…
Geometric singular perturbation theory provides a powerful mathematical framework for the analysis of 'stationary' multiple time-scale systems which possess a critical manifold, i.e. a smooth manifold of steady states for the limiting fast…
The Ginibre ensemble of complex random Hamiltonian matrices $H$ is considered. Each quantum system described by $H$ is a dissipative system and the eigenenergies $Z_{i}$ of the Hamiltonian are complex-valued random variables. For generic…
Three types of blow-up for a fourth-order degenerate reaction-diffusion equation are studied by a combination of analytic and numerical methods. At the critical values of parameters, there occurs a variational problem with a countable set…
The Poincare function is a compact form of counting moduli in local geometric problems. We discuss its property in relation to V.Arnold's conjecture, and derive this conjecture in the case when the pseudogroup acts algebraically and…
In this paper, we establish three Landau-type theorems for certain bounded poly-analytic functions, which generalize the corresponding result for bi-analytic functions given by Liu and Ponnusamy [Canad. Math. Bull. 67(1): 2024, 152-165].…
We solve the problem of resonance statistics in systems with broken time-reversal invariance by deriving the joint probability density of all resonances in the framework of a random matrix approach and calculating explicitly all n-point…
We consider various asymptotic scaling limits $N\to\infty$ for the $2N$ complex eigenvalues of non-Hermitian random matrices in the symmetry class of the symplectic Ginibre ensemble. These are known to be integrable, forming Pfaffian point…
The paper is concerned with the correlation functions of the characteristic polynomials of random matrices with independent complex entries. We investigate how the asymptotic behavior of the correlation functions depends on the second…