Related papers: Concentration inequalities for polynomials of cont…
We study the asymptotic behavior of posterior distributions. We present general posterior convergence rate theorems, which extend several results on posterior convergence rates provided by Ghosal and Van der Vaart (2000), Shen and Wasserman…
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.…
For d>=3, we construct a non-randomized, fair and translation-equivariant allocation of Lebesgue measure to the points of a standard Poisson point process in R^d, defined by allocating to each of the Poisson points its basin of attraction…
Let $\mathbb{H}^{n}=\mathbb{C}^{n}\times\mathbb{R}$ be the $n$-dimensional Heisenberg group, $Q=2n+2$ be the homogeneous dimension of $\mathbb{H}^{n}$. We extend the well-known concentration-compactness principle on finite domains in the…
We investigate the persistence properties of critical d-dimensional systems relaxing from an initial state with non-vanishing order parameter (e.g., the magnetization in the Ising model), focusing on the dynamics of the global order…
In various aspects of the spectral analysis of random Schroedinger operators monotonicity with respect to the randomness plays a key role. In particular, both the continuity properties and the low energy behaviour of the integrated density…
This paper presents new uniform Gaussian strong approximations for empirical processes indexed by classes of functions based on $d$-variate random vectors ($d\geq1$). First, a uniform Gaussian strong approximation is established for general…
We consider random polynomials of the form $G_n(z):= \sum_{|\alpha|\leq n} \xi^{(n)}_{\alpha}p_{n,\alpha}(z)$ where $\{\xi^{(n)}_{\alpha}\}_{|\alpha|\leq n}$ are i.i.d. (complex) random variables and $\{p_{n,\alpha}\}_{|\alpha|\leq n}$ form…
We consider the stochastic Ising model on sparse Erdos-Renyi graphs $G(n,d/n)$ with $d>1$ at the critical temperature $\beta_c=\tanh^{-1}(d^{-1})$ and prove that with high probability, the mixing time is at most polynomial in $n$. Our…
We show that the principal specialization of the Schubert polynomial at $w$ is bounded below by $1+p_{132}(w)+p_{1432}(w)$ where $p_u(w)$ is the number of occurrences of the pattern $u$ in $w$, strengthening a previous result by A.…
We propose a new definition of characteristic polynomials of tensors based on a partition function of Grassmann variables. This new notion of characteristic polynomial addresses general tensors including totally antisymmetric ones, but not…
In this paper we prove that any degree $d$ deformation of a generic logarithmic polynomial differential equation with a persistent center must be logarithmic again. This is a generalization of Ilyashenko's result on Hamiltonian differential…
Today, the Ising model is an archetype describing collective ordering processes. And, as such, it is widely known in physics and far beyond. Less known is the fact that the thesis defended by Ernst Ising 100 years ago (in 1924) contained…
Rates of convergence for empirical risk minimizers have been well studied in the literature. In this paper, we aim to provide a complementary set of results, in particular by showing that after normalization, the risk of the empirical…
We prove global well-posedness and scattering for solutions to the mass-critical inhomogeneous nonlinear Schr\"odinger equation $i\partial_{t}u+\Delta u=\pm |x|^{-b}|u|^{\frac{4-2b}{d}}u$ for large $L^2(\mathbb{R} ^d)$ initial data with…
Concentration properties of functionals of general Poisson processes are studied. Using a modified $\Phi$-Sobolev inequality a recursion scheme for moments is established, which is of independent interest. This is applied to derive moment…
We show that if $\vec X = (X_1, \dots, X_N)$ is a uniform random vector on the unit Euclidean sphere, the empirical CDF of the components of $\sqrt N \vec X = (\sqrt N X_1, \dots, \sqrt N X_N)$ concentrates exponentially rapidly in $N$…
We investigate generalizations of the Charlier and the Meixner polynomials on the lattice N and on the shifted lattice N+1-\beta. We combine both lattices to obtain the bi-lattice N \cup (N+1-\beta) and show that the orthogonal polynomials…
Following the concentration of the measure theory formalism, we consider the transformation $\Phi(Z)$ of a random variable $Z$ having a general concentration function $\alpha$. If the transformation $\Phi$ is $\lambda$-Lipschitz with…
In order to bring contraction analysis into the very fruitful and topical fields of stochastic and Bayesian systems, we extend here the theory describes in \cite{Lohmiller98} to random differential equations. We propose new definitions of…