Related papers: Phenomenological studies in the matrix models

We study the spectral density of factor models of multivariate time series. By making use of the Random Matrix Theory we analytically quantify the effect of noise dressing on the spectral density due to the finiteness of the sample. We…

We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…

In this paper we give a brief review of semiparametric theory, using as a running example the common problem of estimating an average causal effect. Semiparametric models allow at least part of the data-generating process to be unspecified…

In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully…

Topic models analyze text from a set of documents. Documents are modeled as a mixture of topics, with topics defined as probability distributions on words. Inferences of interest include the most probable topics and characterization of a…

We give a mathematical perspective on string compactifications. Submitted as a chapter in the Encyclopedia of Mathematical Physics.

We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…

A growing body of research on probabilistic programs and causal models has highlighted the need to reason compositionally about model classes that extend directed graphical models. Both probabilistic programs and causal models define a…

Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented…

Three subjects are considered here: a self-dual non-critical string that appears in Type IIB superstring theory at points in ${\rm K3}$ moduli space where the Type IIA theory has extended gauge symmetry; a conformal field theory singularity…

We report on progress towards evaluation of stringy non-perturbative effects, using a two dimensional effective field theory for matrix models. We briefly discuss the relevance of such effects to models of dynamical supersymmetry breaking.

In this paper the $c=1$ string theory is studied from the point of view of topological field theories. Calculations are done for arbitrary genus. A change in the prescription is proposed, which reproduces the results of the $1/x^2$ deformed…

In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…

We present a scalable Bayesian model for low-rank factorization of massive tensors with binary observations. The proposed model has the following key properties: (1) in contrast to the models based on the logistic or probit likelihood,…

A survey of the interrelationships between matrix models and field theories on the noncommutative torus is presented. The discretization of noncommutative gauge theory by twisted reduced models is described along with a rigorous definition…

Superstring models describing curved 4-dimensional magnetic flux tube backgrounds are exactly solvable in terms of free fields. We first consider the simplest model of this type (corresponding to `Kaluza-Klein' Melvin background). Its 2d…

This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…

Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…

Pseudo-variograms appear naturally in the context of multivariate Brown-Resnick processes, and are a useful tool for analysis and prediction of multivariate random fields. We give a necessary and sufficient criterion for a matrix-valued…

Risk assessment for rare events is essential for understanding systemic stability in complex systems. As rare events are typically highly correlated, it is important to study heavy-tailed multivariate distributions of the relevant…