Related papers: Generalized multicritical one-matrix models
We propose the Kazakov-Migdal model on graphs and show that, when the parameters of this model are appropriately tuned, the partition function is represented by the unitary matrix integral of an extended Ihara zeta function, which has a…
An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs.…
We study the problem of reconstructing a function on a manifold satisfying some mild conditions, given data on the values and some derivatives of the function at arbitrary points on the manifold. While the problem of finding a polynomial of…
We prove a formula for the multidegrees of a rational map defined by generalized monomials on a projective variety, in terms of integrals over an associated Newton region. This formula leads to an expression of the multidegrees as volumes…
Kontsevitch's work on Airy matrix integrals has led to explicit results for the intersection numbers of the moduli space of curves. In a subsequent work Okounkov rederived these results from the edge behavior of a Gaussian matrix integral.…
Starting from any finite simple graph, one can build a reflexive polytope known as a symmetric edge polytope. The first goal of this paper is to show that symmetric edge polytopes are intrinsically matroidal objects: more precisely, we…
Analytic interpolation problems with rationality and derivative constraints occur in many applications in systems and control. In this paper we present a new method for the multivariable case, which generalizes our previous results on the…
Multilinear interpolation is a powerful tool used in obtaining strong type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear…
Given multigraded free resolutions of two monomial ideals we construct a multigraded free resolution of the sum of the two ideals.
The classical polynomial interpolation problem in several variables can be generalized to the case of points with greater multiplicities. What is known, as yet, is essentially concentrated in the Alexander-Hirschowitz Theorem which says…
We give a combinatorial classification for the class of postcritically fixed Newton maps of polynomials and indicate potential for extensions. As our main tool, we show that for a large class of Newton maps that includes all hyperbolic…
We characterize monomial ideals which are intersections of monomial prime ideals and study classes of ideals with this property, among them polymatroidal ideals.
In this article, we study in detail the modified topological recursion of the one matrix model for arbitrary $\beta$ in the one cut case. We show that for polynomial potentials, the recursion can be computed as a sum of residues. However…
Solutions to the Markov equation appear in many mathematical contexts. We aim to build on the understanding of them by proving a recent conjecture about Markov polynomials; solutions to a generalised version of the Markov equation. The…
We obtain an improvement and broad generalisation of a result of N. Ailon and Z. Rudnick (2004) on common zeros of shifted powers of polynomials. Our approach is based on reducing this question to a more general question of counting…
In this paper we introduce generalised Markov numbers and extend the classical Markov theory for the discrete Markov spectrum to the case of generalised Markov numbers. In particular we show recursive properties for these numbers and find…
In this paper we study the consequences of overinterpolation, i.e., the situation when a function can be interpolated by polynomial, or rational, or algebraic functions in more points that normally expected. We show that in many cases such…
Univariate delta Gon\v{c}arov polynomials arise when the classical Gon\v{c}arov interpolation problem in numerical analysis is modified by replacing derivatives with delta operators. When the delta operator under consideration is the…
We investigate polynomials, called m-polynomials, whose generator polynomial has coefficients that can be arranged as a matrix, where q is a positive integer greater than one. Orthogonality relations are established and coefficients are…
The classical matrix tree theorem relates the number of spanning trees of a connected graph with the product of the nonzero eigenvalues of its Laplacian matrix. The class of regular matroids generalizes that of graphical matroids, and a…