Related papers: Szeg\H{o} type correlations for two-dimensional ou…
We continue to investigate some classes of Szeg\"o type polynomials in several variables. We focus on asymptotic properties of these polynomials and we extend several classical results of G. Szeg\"o to this setting.
We consider triangular holes on the hexagonal lattice and we study their interaction when the rest of the lattice is covered by dimers. More precisely, we analyze the joint correlation of these triangular holes in a ``sea'' of dimers. We…
We establish versions of Szeg\H{o}'s distance formula and Widom's theorem on invertibility of (a family of) Toeplitz operators in a class of finite codimension subalgebras of uniform algebras, obtained by imposing a finite number of linear…
This paper is devoted to a study of $S$-curves, that is systems of curves in the complex plane whose equilibrium potential in a harmonic external field satisfies a special symmetry property ($S$-property). Such curves have many…
Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…
Recent numerical and analytical work has shown that for the square-lattice Heisenberg model the boundary can induce Dimer correlations near the edge which are absent in spin-wave theories and non-linear sigma model approaches. Here, we…
We construct a pointwise Boutet de Monvel-Sj\"ostrand parametrix for the Szeg\H{o} kernel of a weakly pseudoconvex three dimensional CR manifold of finite type assuming the range of its tangential CR operator to be closed; thereby extending…
We give conjectures on the "asymptotic" behaviour of the Hilbert series of (quotients by) generic ideals in the exterior algebra, as the number of variables tend to infinity. Our conjectures are supported by extensive computer calculations.
We consider symmetric partial exclusion and inclusion processes in a general graph in contact with reservoirs, where we allow both for edge disorder and well-chosen site disorder. We extend the classical dualities to this context and then…
Based on large-scale quantum Monte Carlo simulations, we examine the correlations along the edges of two-dimensional semi-infinite quantum critical Heisenberg spin-$1/2$ systems. In particular, we consider coupled quantum spin-dimer systems…
We study the temperature dependence of static and dynamic responses of Coulomb interacting particles in two-dimensional traps across the thermal crossover from an amorphous solid- to liquid-like behaviors. While static correlations, that…
We analyze collective excitations in models of two-dimensional topological insulators using the random phase approximation. In a two-dimensional extension of the Su-Schrieffer-Heeger model, edge plasmonic excitations with induced…
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…
A discrete Gelfand-Tsetlin pattern is a configuration of particles in Z^2. The particles are arranged in a finite number of consecutive rows, numbered from the bottom. There is one particle on the first row, two particles on the second row,…
We impose the uniform probability measure on the set of all discrete Gelfand-Tsetlin patterns of depth $n$ with the particles on row $n$ in deterministic positions. These systems equivalently describe a broad class of random tilings models,…
We theoretically investigate the Coulomb drag between the edge states of two quantum spin Hall systems. Using an interacting theory of the one-dimensional helical edge modes, we show that the drag vanishes at second order in the inter-edge…
We investigate the asymptotic behaviour of the second-order correlation function of the characteristic polynomial of a Hermitian Wigner matrix at the edge of the spectrum. We show that the suitably rescaled second-order correlation function…
We provide a representation in terms of certain canonical functions for a sequence of polynomials orthogonal with respect to a weight that is strictly positive and analytic on the unit circle. These formulas yield a complete asymptotic…
H. Widom derived formulae expressing correlation functions of orthogonal and symplectic ensembles of random matrices in terms of orthogonal polynomials (H. Widom. J. Stat. Phys. 94, (1999) 347-363). We obtain similar results for discrete…
We make use of continuum elasticity theory to investigate the collective modes that propagate along the edge of a two-dimensional electron liquid or crystal in a magnetic field. An exact solution of the equations of motion is obtained with…