相关论文: Subgaussian sequences in probability and Fourier a…

The goal of this paper is to construct a Frobenius splitting on $G/U$ via the Poisson geometry of $(G/U,\pi_{G/U})$, where $G$ is a semi-simple algebraic group of classical type defined over an algebraically closed field of characteristic…

Consider the algebraic dynamics on a torus T=G_m^n given by a matrix M in GL_n(Z). Assume that the characteristic polynomial of M is prime to all polynomials X^m-1. We show that any finite equivariant map from another algebraic dynamics…

In this paper we consider a Bayesian framework for making inferences about dynamical systems from ergodic observations. The proposed Bayesian procedure is based on the Gibbs posterior, a decision theoretic generalization of standard…

We present a simple solution to a question posed by Candes, Romberg and Tao on the uniform uncertainty principle for Bernoulli random matrices. More precisely, we show that a rectangular k*n random subgaussian matrix (with k < n) has the…

Inspired by the analysis of variance (ANOVA) decomposition of functions we propose a Gaussian-Uniform mixture model on the high-dimensional torus which relies on the assumption that the function we wish to approximate can be well explained…

Analysis of low-degree polynomial algorithms is a powerful, newly-popular method for predicting computational thresholds in hypothesis testing problems. One limitation of current techniques for this analysis is their restriction to…

This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…

We give a simple example of an $n$-tuple of orthonormal elements in $L_2$ (actually martingale differences) bounded by a fixed constant, and hence subgaussian with a fixed constant but that are Sidon only with constant $\approx \sqrt n$.…

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…

We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…

Random matrices acting on structured sets play a fundamental role in high-dimensional geometry, compressed sensing, and randomized algorithms. Existing results primarily focus on subgaussian models, when random matrices act as…

Using sequences of finite length with positive integer elements and the inversion statistic on such sequences, a collection of binomial and multinomial identities are extended to their $q$-analog form via combinatorial proofs. Using the…

Mixtures of Gaussian Bayesian networks have previously been studied under full-covariance assumptions, where each mixture component has its own covariance matrix. We propose a mixture model with tied-covariance, in which all components…

Several classical results on boundary crossing probabilities of Brownian motion and random walks are extended to asymptotically Gaussian random fields, which include sums of i.i.d. random variables with multidimensional indices,…

This note provides a basic description of subgaussianity, by defining $(\sigma, \rho)$-subgaussian random variables $X$ ($\sigma>0, \rho>0$) as those satisfying $\mathbb{E}(\exp(\lambda X))\leq \rho\exp(\frac{1}{2}\sigma^2\lambda^2)$ for…

In [1] a new bosonization procedure has been illustrated, which allows to express a fermionic gaussian system in terms of commuting variables at the price of introducing an extra dimension. The Fermi-Bose duality principle established in…

We give an exposition of some connections between Fourier optimization problems and problems in number theory. In particular, we present some recent conditional bounds under the generalized Riemann hypothesis, achieved via a Fourier…

We consider the problem of detecting (testing) Gaussian stochastic sequences (signals) with imprecisely known means and covariance matrices. The alternative is independent identically distributed zero-mean Gaussian random variables with…

Consider a sequence of Gibbsian line ensembles, whose lowest labeled curves (i.e., the edge) have tight one-point marginals. Then, given certain technical assumptions on the nature of the Gibbs property and underlying random walk measure,…

The aim of this paper is to give a precise asymptotic description of some eigenvalue statistics stemming from random matrix theory. More precisely, we consider random determinants of the GUE, Laguerre, Uniform Gram and Jacobi beta ensembles…