相关论文: Relative volume of comparable pairs under semigrou…

We consider the predictive problem of supervised ranking, where the task is to rank sets of candidate items returned in response to queries. Although there exist statistical procedures that come with guarantees of consistency in this…

Synchronized measurements of a large power grid enable an unprecedented opportunity to study the spatialtemporal correlations. Statistical analytics for those massive datasets start with high-dimensional data matrices. Uncertainty is…

This paper focuses on the prominent sphericity test when the dimension $p$ is much lager than sample size $n$. The classical likelihood ratio test(LRT) is no longer applicable when $p\gg n$. Therefore a Quasi-LRT is proposed and asymptotic…

Let X_N= (X_1^(N), ..., X_p^(N)) be a family of N-by-N independent, normalized random matrices from the Gaussian Unitary Ensemble. We state sufficient conditions on matrices Y_N =(Y_1^(N), ..., Y_q^(N)), possibly random but independent of…

We study semiorders induced by points drawn from a uniform random distribution. Of particular interest in this paper are the probabilities of generating specific semiorders and the equivalence classes they produce. We present a method for…

We study the problem of maximizing the probability that (i) an electric component or financial institution $X$ does not default before another component or institution $Y$ and (ii) that $X$ and $Y$ default jointly within the class of all…

We briefly review the random matrix theory for large N by N matrices viewed as free random variables in a context of stochastic diffusion. We establish a surprising link between the spectral properties of matrix-valued multiplicative…

Many natural notions of additive and multiplicative largeness arise from results in Ramsey theory. In this paper, we explain the relationships between these notions for subsets of $\mathbb{N}$ and in more general ring-theoretic structures.…

We establish asymptotic formulae for general joint moments of characteristic polynomials and their higher-order derivatives associated with matrices drawn randomly from the groups $\mathrm{USp}(2N)$ and $\mathrm{SO}(2N)$ in the limit as…

We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with…

Unification of matter fields implies the existence of accidental permutation symmetries, which potentially remain immune to large quantum corrections up to the TeV scale. We investigate the case of a supersymmetric $SU(5)$ grand unified…

A probability measure $P_n$ on the symmetric group ${\mathfrak S}_n$ is said to be record-dependent if $P_n(\sigma)$ depends only on the set of records of a permutation $\sigma\in{\mathfrak S}_n$. A sequence $P=(P_n)_{n\in{\mathbb N}}$ of…

This paper is on developing stochastic analysis simultaneously under a general family of probability measures that are not dominated by a single probability measure. The interest in this question originates from the probabilistic…

We use classical results from harmonic analysis on matrix spaces to investigate the relation between the joint density of the singular values and of the eigenvalues of complex random matrices which are bi-unitarily invariant (also known as…

This paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxations to solve it globally. Under some assumptions, we prove…

The purpose of this note is to study asymptotic zero distribution of multivariate random polynomials as their degrees grow. For a smooth weight function with super logarithmic growth at infinity, we consider random linear combinations of…

Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…

In this paper, we study majorization for probability distributions and column stochastic matrices. We show that majorizations in general can be reduced to the aforementioned sets. We characterize linear operators that preserve majorization…

Given a semigroup $S$ and an $n$-partition $\mathcal{P}$ of $S$, $n\in \mathbb{N}$, do there exist $A\in \mathcal{P}$ and a subset $F$ of $S$ such that $S=F ^{-1} \{x \in S: x A \bigcap A\neq\emptyset\}$ and $|F |\leq n$? We give an…

We develop an information-theoretic view of the stochastic block model, a popular statistical model for the large-scale structure of complex networks. A graph $G$ from such a model is generated by first assigning vertex labels at random…