相关论文: Challenges of Matrix Models

We briefly review the connection between the fuzzy field theories and matrix models and describe the main features of the models that appear. We summarize the different approaches to their analysis, some of the recent results and the…

We present a treasure trove of open problems in matrix and operator inequalities, of a functional analytic nature, and with various degrees of hardness.

The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, ``conformal'' (multicomponent) and Kontsevich models are considered in some detail, together with the…

The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Determinantal formulas, relation to conformal field models and the theory of Generalized Kontsevich model are discussed in some…

A unified matrix-vector representation is developed of such solution concepts as the core, the uncovered, the uncaptured, the minimal weakly stable, the minimal undominated, the minimal dominant and the untrapped sets. We also propose…

In this note we briefly survey and propose some open problems related to isoparametric theory.

Presentation of set matrices and demonstration of their efficiency as a tool using the path/cycle problem.

This is a presentation of recent work on quantum permutation groups, complex Hadamard matrices, and the connections between them. A long list of problems is included. We include as well some conjectural statements, about matrix models.

We discuss various problems in frame theory that have been open for some years. A short discussion of frame theory is also provided, but it only contains the information that is necessary in order to understand the open problems and their…

We summarize some aspects of matrix models from the approaches directly based on their properties at finite N.

A short review of the recent results and models of complex networks.

We discuss several aspects of creation of adequate mathematical models in other sciences. In particular, many difficulties stem from great complexity of the source systems and the presence of a variety of uncertain factors. We illustrate…

In this short paper, we study some trace inequalities of the products of the matrices and the power of matrices by the use of elementary calculations.

We review recent developments in the theory of supermembranes and their relation to matrix models.

An essay on Model Theory: Why am I interested in model theory? What are, in my opinion, the most challenging problems in model theory?

We review recent developments in the theory of supermembranes and their relation to matrix models.

In this article, we show multiple inequalities for the singular values of the difference of matrix means. The obtained results refine and complement some well established results in the literature. Although we target singular values…

We propose several open problems on GKK tau-matrices raised by examples showing that some such matrices are unstable

Some exact solutions to the classical matrix model equations that arise in the context of M(embrane) theory are given, and their topological nature is identified.

We describe a list of open problems in random matrix theory and the theory of integrable systems that was presented at the conference Asymptotics in Integrable Systems, Random Matrices and Random Processes and Universality, Centre de…