相关论文: On the singular sector of the Hermitian random mat…
We consider a parameter dependent ensemble of two real random matrices with Gaussian distribution. It describes the transition between the symmetry class of the chiral Gaussian orthogonal ensemble (Cartan class B$|$DI) and the ensemble of…
In this paper, we consider the near-critical dimer model in the setup of isoradial superpositions with Temperleyan boundary conditions. We show that the centered height function converges as the mesh size tends to zero to a limiting field…
A hodograph transformation for a wide family of multidimensional nonlinear partial differential equations is presented. It is used to derive solutions of the heavenly equation (dispersionless Toda equation) as well as a family of explicit…
Using the Hirota representation of dispersionless dKP and dToda hierarchies, we show that the chordal L\"owner equations and radial L\"owner equations respectively serve as consistency conditions for one variable reductions of these…
We study a non-Hermitian (NH) $sl(2)$ affine Toda model coupled to fermions through soliton theory techniques and the realizations of the pseudo-chiral and pseudo-Hermitian symmetries. The interplay of non-Hermiticity, integrability,…
We review the integrable structure of the Dirichlet boundary problem in two dimensions. The solution to the Dirichlet boundary problem for simply-connected case is given through a quasiclassical tau-function, which satisfies the Hirota…
We present and investigate a general model for inhomogeneous random digraphs with labeled vertices, where the arcs are generated independently, and the probability of inserting an arc depends on the labels of its endpoints and its…
What is the connection of random matrices with integrable systems? Is this connection really useful? Introducing apprpriate times in the distribution of the ensemble of matrices, one shows that the corresponding distribution of the…
In this letter we present, in a number conserving framework, a model of interacting fermions in a two-wire geometry supporting non-local zero-energy Majorana-like edge excitations. The model has an exactly solvable line, on varying the…
The bulk-boundary correspondence predicts the existence of boundary modes localized at the edges of topologically nontrivial systems. The wavefunctions of hermitian boundary modes can be obtained as the eigenmodes of a modified Jackiw-Rebbi…
Let $X$ be a weakly pseudoconvex manifold and $L\longrightarrow X$ be a holomorphic line bundle with a singular positive Hermitian metric $h$. In this article, we provide a points separation theorem and an embedding for the adjoint linear…
Random matrix models encode a theory of random two dimensional surfaces with applications to string theory, conformal field theory, statistical physics in random geometry and quantum gravity in two dimensions. The key to their success lies…
A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…
Joint distribution function of N eigenvalues of U(N) invariant random-matrix ensemble can be interpreted as a probability density to find N fictitious non-interacting fermions to be confined in a one-dimensional space. Within this picture a…
We study $N \times N$ random band matrices $H = (H_{xy})$ with mean-zero complex Gaussian entries, where $x,y$ lie on the discrete torus $(\mathbb{Z} / \sqrt[d]{N} \mathbb{Z})^d$ in dimensions $d \ge 3$. The variance profile satisfies…
We introduce random matrix ensembles that correspond to the infinite families of irreducible Riemannian symmetric spaces of type I. In particular, we recover the Circular Orthogonal and Symplectic Ensembles of Dyson, and find other families…
We consider the hermitian random matrix model with external source and general polynomial potential, when the source has two distinct eigenvalues but is otherwise arbitrary. All such models studied so far have a common feature: an…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
This paper reconsiders finite variable reductions of the universal Whitham hierarchy of genus zero in the perspective of dispersionless Hirota equations. In the case of one-variable reduction, dispersionless Hirota equations turn out to be…
The dispersionless KP and Toda hierarchies possess an underlying twistorial structure. A twistorial approach is partly implemented by the method of Riemann-Hilbert problem. This is however still short of clarifying geometric ingredients of…