相关论文: Thin sets of integers in Harmonic analysis and p-s…

We show how different random thin sets of integers may have different behaviour. First, using a recent deviation inequality of Boucheron, Lugosi and Massart, we give a simpler proof of one of our results in {\sl Some new thin sets of…

We randomly construct various subsets $\Lambda$ of the integers which have both smallness and largeness properties. They are small since they are very close, in various meanings, to Sidon sets: the continuous functions with spectrum in…

We study the regularity of densities of distributions that are polynomial images of the standard Gaussian measure on $\mathbb{R}^n$. We assume that the degree of a polynomial is fixed and that each variable enters to a power bounded by…

Linear combinations of translations of a single Gaussian, e^{-x^2}, are shown to be dense in L^2(R). Two algorithms for determining the coefficients for the approximations are given, using orthogonal Hermite functions and least squares.…

We study a system of $N$ qubits with a random Hamiltonian obtained by drawing coupling constants from Gaussian distributions in various ways. This results in a rich class of systems which include the GUE and the fixed $q$ SYK theories. Our…

We define a natural notion of higher order stability and show that subsets of $\mathbb{F}_p^n$ that are tame in this sense can be approximately described by a union of low-complexity quadratic varieties, up to linear error. This generalizes…

We study how to estimate a nearly low-rank Toeplitz covariance matrix $T$ from compressed measurements. Recent work of Qiao and Pal addresses this problem by combining sparse rulers (sparse linear arrays) with frequency finding (sparse…

A theorem of Waldspurger states that the Fourier transform of a stable distribution on the Lie algebra of a simply-connected semisimple group $G$ over a p-adic field, is again stable. We generalize this theorem to representations whose…

We give a precise measure of the rate at which repeated differentiation of a random trigonometric polynomial causes the roots of the function to approach equal spacing. This can be viewed as a toy model of crystallization in one dimension.…

On a probability space $(\Omega, \mathcal F, \mathbb P)$ we consider two independent sequences $(a_k)_{k \geq 1}$ and $(b_k)_{k \geq 1}$ of i.i.d. random variables that are centered with unit variance and which admit a moment strictly…

We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k << N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic…

Observables in random tensor theory are polynomials in the entries of a tensor of rank $d$ which are invariant under $U(N)^d$. It is notoriously difficult to evaluate the expectations of such polynomials, even in the Gaussian distribution.…

The relationship between a stable multivariable polynomial $p(z)$ and the Fourier coefficients of its spectral density function $1/|p(z)|^2$, is further investigated. In this paper we focus on the radial asymptotics of the Fourier…

We prove that for all p>1/2 there exists a constant $\gamma_p>0$ such that, for any symmetric measurable set of positive measure $E\subset \TT$ and for any $\gamma<\gamma_p$, there is an idempotent trigonometrical polynomial f satisfying…

Andreas Maurer in the paper "A vector-contraction inequality for Rademacher complexities" extended the contraction inequality for Rademacher averages to Lipschitz functions with vector-valued domains; He did it replacing the Rademacher…

Recently, it has been observed that a sparse trigonometric polynomial, i.e. having only a small number of non-zero coefficients, can be reconstructed exactly from a small number of random samples using Basis Pursuit (BP) or Orthogonal…

For dispersive Hamiltonian partial differential equations of order 2N+1, N integer, there are two criteria to analyse to examine the stability of small-amplitude, periodic travelling wave solutions to high-frequency perturbations. The first…

Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…

We give a strongly polynomial-time algorithm for integer linear programs defined by integer coefficient matrices whose subdeterminants are bounded by a constant and that contain at most two nonzero entries in each row. The core of our…

This paper considers regularizing a covariance matrix of $p$ variables estimated from $n$ observations, by hard thresholding. We show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is…