Related papers: Punctures and p-spin curves from matrix models II
The arithmetic of elliptic curves, namely polynomial addition and scalar multiplication, can be described in terms of global sections of line bundles on $E\times E$ and $E$, respectively, with respect to a given projective embedding of $E$…
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…
In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…
We consider a large class of bullet models that contains, in particular, the colliding bullet model with creations and a new loop model. For this large class of bullet models, we give sufficient conditions on their parameter to be…
We obtain new concavity results, up to a suitable transformation, for a class of quasi-linear equations in a convex domain involving the $p$-Laplace operator and a general nonlinearity satisfying concavity type assumptions. This provides an…
In this article, we combine Bhargava's geometry-of-numbers methods with the dynamical point-counting methods of Eskin--McMullen and Benoist--Oh to develop a new technique for counting integral points on symmetric varieties lying within…
A spin-space extension is reviewed, which provides information on the standard model. Its defining feature is a common matrix space that describes symmetries and representations, and leads to limits on these, for given dimension. The model…
We study the cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we show that there is a bijection between tagged curves and string objects. Applications include…
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…
We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the…
We consider a pair of isoperimetric problems arising in physics. The first concerns a Schr\"odinger operator in $L^2(\mathbb{R}^2)$ with an attractive interaction supported on a closed curve $\Gamma$, formally given by $-\Delta-\alpha…
This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…
Data-driven reduced order models (ROMs) recently emerged as powerful tool for the solution of inverse scattering problems. The main drawback of this approach is that it was limited to the measurement arrays with reciprocally collocated…
We generalize the result of Voronov (1988) to give an expression for the super Mumford form $\mu$ on the moduli spaces of super Riemann surfaces with Ramond and Neveu-Schwarz punctures in the limit where the number of punctures is large…
The p-spin spin-glass model has been studied extensively at mean-field level because of the insights which it provides into the mode-coupling approach to structural glasses and the nature of the glass transition. We demonstrate explicitly…
We develop quaternion--native iterative methods for computing the Moore--Penrose (MP) pseudoinverse of quaternion matrices and analyze their convergence. Our starting point is a damped Newton--Schulz (NS) iteration tailored to…
We study the approximability of computing the partition functions of two-state spin systems. The problem is parameterized by a $2\times 2$ symmetric matrix. Previous results on this problem were restricted either to the case where the…
For small odd primes $p$, we prove that most of the rational points on the modular curve $X_0(p)/w_p$ parametrize pairs of elliptic curves having infinitely many supersingular primes. This result extends the class of elliptic curves for…
In this paper we study algorithmic aspects of tropical intersection theory. We analyse how divisors and intersection products on tropical cycles can actually be computed using polyhedral geometry. The main focus of this paper is the study…
The analysis of high-precision $\pi^{\pm}p \to \pi^{\pm}p$ cross section data from the EPECUR Collaboration based on the multichannel $K$-matrix approach is presented.The sharp structures seen in these data are studied in terms of both…