相关论文: Some open problems in random matrix theory and the…

These are lectures notes for a 4h30 mini-course held in Ulaanbaatar, National University of Mongolia, August 5-7th 2015, at the summer school "Stochastic Processes and Applications". It aims at presenting an introduction to basic results of…

We present a list of open questions in the theory of holomorphic foliations, possibly with singularities. Some problems have been around for a while, others are very accessible.

We discuss the question of how to pick a matrix uniformly (in an appropriate sense) at random from groups big and small. We give algorithms in some cases, and indicate interesting problems in others.

This review article provides an overview of random matrix theory (RMT) with a focus on its growing impact on the formulation and inference of statistical models and methodologies. Emphasizing applications within high-dimensional statistics,…

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

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…

Here we clarify few important issues raised in the recent cond-mat/0204241.

We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…

This is a very brief review of relations between Seiberg-Witten theories and integrable systems with emphasis on the perturbative prepotentials presented at the E.S.Fradkin Memorial Conference.

This chapter is an introduction to the connection between random matrices and maps, i.e graphs drawn on surfaces. We concentrate on the one-matrix model and explain how it encodes and allows to solve a map enumeration problem.

The concept of structural invariance previously introduced by the authors is used to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the…

Random matrix theory (RMT) provides a common mathematical formulation of distinct physical questions in three different areas: quantum chaos, the 1-d integrable model with the $1/r^2$ interaction (the Calogero-Sutherland-Moser system), and…

This paper considers random (non-Hermitian) circulant matrices, and proves several results analogous to recent theorems on non-Hermitian random matrices with independent entries. In particular, the limiting spectral distribution of a random…

The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…

This list of problems arose as a collaborative effort among the participants of the Arbeitsgemeinschaft on Mathematical Quasicrystals, which was held at the Mathematisches Forschungsinstitut Oberwolfach in October 2015. The purpose of our…

This contribution to the proceedings of the Cracow meeting on `Applications of Random Matrix Theory' summarizes a series of studies, some old and others more recent on financial applications of Random Matrix Theory (RMT). We first review…

In this note, we propose some open problems and questions about bounded convex domains in $\mathbb C^N$, specifically about visibility and iteration theory.

This report summarizes some of the material that was presented by the author during the 2015 Les Houches Summerschool on "Random Matrices and Stochastic Processes". In these Lectures, various applications of Random Matrix Theory in modern…

Randomstrasse101 is a blog dedicated to Open Problems in Mathematics, with a focus on Probability Theory, Computation, Combinatorics, Statistics, and related topics. This manuscript serves as a stable record of the Open Problems posted in…

$\texttt{Randomstrasse101}$ is a blog dedicated to Open Problems in Mathematics, with a focus on Probability Theory, Computation, Combinatorics, Statistics, and related topics. This manuscript serves as a stable record of the Open Problems…