相关论文: Random Matrices, the Ulam Problem, Directed Polyme…
Many practical optimization problems lack strong convexity. Fortunately, recent studies have revealed that first-order algorithms also enjoy linear convergences under various weaker regularity conditions. While the relationship among…
We survey recent (and not so recent) results concerning arrangements of lines, points and other geometric objects and the applications these results have in theoretical computer science and combinatorics. The three main types of problems we…
We consider $N\times N$ random matrices of the form $H = W + V$ where $W$ is a real symmetric Wigner matrix and $V$ a random or deterministic, real, diagonal matrix whose entries are independent of $W$. We assume subexponential decay for…
While deep learning is successful in a number of applications, it is not yet well understood theoretically. A satisfactory theoretical characterization of deep learning however, is beginning to emerge. It covers the following questions: 1)…
We discuss recently discovered links of the statistical models of normal random matrices to some important physical problems of pattern formation and to the quantum Hall effect. Specifically, the large $N$ limit of the normal matrix model…
The problem of pattern selection arises when the evolution equations have many solutions, whereas observed patterns constitute a much more restricted set. An approach is advanced for treating the problem of pattern selection by defining the…
Mathematical modeling is a standard approach to solve many real-world problems and {\em diversity} of solutions is an important issue, emerging in applying solutions obtained from mathematical models to real-world problems. Many studies…
We obtain the asymptotic behaviour of the longest increasing/non-decreasing subsequences in a random uniform multiset permutation in which each element in {1,...,n} occurs k times, where k may depend on n. This generalizes the famous…
Since it was first applied to the study of nuclear interactions by Wigner and Dyson, almost 60 years ago, Random Matrix Theory (RMT) has developed into a field of its own within applied mathematics, and is now essential to many parts of…
Let the sample correlation matrix be $W=YY^T$, where $Y=(y_{ij})_{p,n}$ with $y_{ij}=x_{ij}/\sqrt{\sum_{j=1}^nx_{ij}^2}$. We assume $\{x_{ij}: 1\leq i\leq p, 1\leq j\leq n\}$ to be a collection of independent symmetric distributed random…
We introduce the Random Subsequence Model, a spin glass model on pairs of random strings $(X,Y) \in \{0,1\}^N \times \{0,1\}^M$ whose partition function counts subsequence embeddings of $Y$ into $X$. We study two variants: the null model,…
It is described how one comes to the Wigner-Dyson random matrix theory (RMT) starting from a model of a disordered metal. The lectures start with a historical introduction where basic ideas of the RMT and theory of disordered metals are…
In this review paper we consider the polynuclear growth (PNG) model in one spatial dimension and its relation to random matrix ensembles. For curved and flat growth the scaling functions of the surface fluctuations coincide with limit…
This is a review of the Riemann-Hilbert approach to the large $N$ asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
Neural network models and deep models are one of the leading and state of the art models in machine learning. Most successful deep neural models are the ones with many layers which highly increases their number of parameters. Training such…
Unimodular sequences with good auto/cross-correlation properties are favorable in wireless communication and radar applications. In this paper, we focus on designing these kinds of sequences. The main content is as follows: first, we…
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…
Signatures of universality are detected by comparing individual eigenvalue distributions and level spacings from financial covariance matrices to random matrix predictions. A chopping procedure is devised in order to produce a statistical…
Linear problems appear in a variety of disciplines and their application for the transmission matrix recovery is one of the most stimulating challenges in biomedical imaging. Its knowledge turns any random media into an optical tool that…