Related papers: Higher Genus Correlators for the Complex Matrix Mo…

Estimation of generalized linear mixed models (GLMMs) with non-nested random effects structures requires approximation of high-dimensional integrals. Many existing methods are tailored to the low-dimensional integrals produced by nested…

We calculate connected correlators in time dependent Gaussian orthogonal and symplectic random matrix ensembles by a diagrammatic method. We obtain averaged one-point Green's functions in the leading order O(1) and wide two-level and…

This paper introduces a method for studying the correlation structure of a range of responses modelled by a multivariate generalised linear mixed model (MGLMM). The methodology requires the existence of clusters of observations and that…

Following the program, proposed in hep-th/0310113, of systematizing known properties of matrix model partition functions (defined as solutions to the Virasoro-like sets of linear differential equations), we proceed to consideration of…

We use the explicit relation between genus filtrated $s$-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich--Penner matrix model (KPMM), which is the generating function for volumes of discretized…

We propose a generalization of the Quantum Monte Carlo loop algorithm to the t-J model by a mapping to three coupled six-vertex models. The autocorrelation times are reduced by orders of magnitude compared to the conventional local…

Latent factor models that integrate data from multiple sources/studies or modalities have garnered considerable attention across various disciplines. However, existing methods predominantly focus either on multi-study integration or…

A novel algorithm for computing the action of a matrix exponential over a vector is proposed. The algorithm is based on a multilevel Monte Carlo method, and the vector solution is computed probabilistically generating suitable random paths…

We develop a new framework to compute the exact correlators of characteristic polynomials, and their inverses, in random matrix theory. Our results hold for general potentials and incorporate the effects of an external source. In matrix…

I consider the Hermitean two-matrix model with a logarithmic potential which is associated in the one-matrix case with the Penner model. Using loop equations I find an explicit solution of the model at large N (or in the spherical…

We introduce a novel multivariate GARCH model with flexible convolution-t distributions that is applicable in high-dimensional systems. The model is called Cluster GARCH because it can accommodate cluster structures in the conditional…

Generalized unitarity cut of a Feynman diagram generates an algebraic system of polynomial equations. At high-loop levels, these equations may define a complex curve or a (hyper-)surface with complicated topology. We study the curve cases,…

The tree-level S-matrix of type II supergravity can be computed in scattering equation form by correlators in a worldsheet theory analogous to a chiral, infinite tension limit of the pure spinor formalism. By defining a non-minimal version…

We outline a general algorithm for computing an explicit model over a number field of any curve of genus 2 whose (unpolarized) Jacobian is isomorphic to the product of two elliptic curves with CM by the same order in an imaginary quadratic…

We show that many infinite classes of permutations over finite fields can be constructed via translators with a large choice of parameters. We first charac- terize some functions having linear translators, based on which several families of…

The loop equations for a chain of hermitian random matrices are computed explicitely, including the 1/N^2 corrections. To leading order, the master loop equation reduces to an algebraic equation, whose solution can be written in terms of…

Complex analysis is a powerful tool to study classical integrable systems, statistical physics on the random lattice, random matrix theory, topological string theory,... All these topics share certain relations, called "loop equations" or…

An algorithm for calculating two-loop propagator type Feynman diagrams with arbitrary masses and external momentum is proposed. Recurrence relations allowing to express any scalar integral in terms of basic integrals are given. A minimal…

We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization…

We compute higher-point superstring correlators involving spin fields in various even space-time dimensions D at tree-level and to arbitrary loop order. This generalizes previous work in D=4 space-time dimensions. The main focus are D=6,8…