Related papers: A Maxwell principle for generalized Orlicz balls

This note contains two types of small ball estimates for random vectors in finite dimensional spaces equipped with a quasi-norm. In the first part, we obtain bounds for the small ball probability of random vectors under some smoothness…

We study the small ball probability of an order-$\ell$ simple random tensor $X=X^{(1)}\otimes\cdots\otimes X^{(\ell)}$ where $X^{(i)}, 1\leq i\leq\ell$ are independent random vectors in $\mathbb{R}^n$ that are log-concave or have…

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…

We study the problem of testing, using only a single sample, between mean field distributions (like Curie-Weiss, Erd\H{o}s-R\'enyi) and structured Gibbs distributions (like Ising model on sparse graphs and Exponential Random Graphs). Our…

By using a reductive perturbation method, we derive from Maxwell-Bloch equations a cubic generalized Kadomtsev-Petviashvili equation for ultrashort spatiotemporal optical pulse propagation in cubic (Kerr-like) media without the use of the…

This paper is concerned with the study of a circular random distribution called geodesic Normal distribution recently proposed for general manifolds. This distribution, parameterized by two real numbers associated to some specific location…

Let ${\mathbb X}$ be a compact, connected, Riemannian manifold (without boundary), $\rho$ be the geodesic distance on ${\mathbb X}$, $\mu$ be a probability measure on ${\mathbb X}$, and $\{\phi_k\}$ be an orthonormal system of continuous…

The problem of determining a periodic Lipschitz vector field $b=(b_1, \dots, b_d)$ from an observed trajectory of the solution $(X_t: 0 \le t \le T)$ of the multi-dimensional stochastic differential equation \begin{equation*} dX_t =…

In this paper we provide a detailed study on effective versions of the celebrated Bilu's equidistribution theorem for Galois orbits of sequences of points of small height in the $N$-dimensional algebraic torus, identifying the quantitative…

In this paper, we prove that the Euclidean distance between two independent random vectors uniformly distributed on $l_p^n$-balls $(1 \leq p \leq \infty)$ or on its boundary satisfies a central limit theorem as $n$ tends to $\infty$. Also,…

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N stochastic variables with Lochner's generalized Dirichlet distribution (R.H. Lochner, A Generalized…

Given a star-shaped domain $K\subseteq \mathbb R^d$, $n$ vectors $v_1,\dots,v_n \in \mathbb R^d$, a number $R>0$, and i.i.d. random variables $\eta_1,\dots,\eta_n$, we study the geometric and arithmetic structure of the set of vectors $V =…

Small ball inequalities have been extensively studied in the setting of Gaussian processes and associated Banach or Hilbert spaces. In this paper, we focus on studying small ball probabilities for sums or differences of independent,…

This paper establishes complete convergence for weighted sums and the Marcinkiewicz--Zygmund-type strong law of large numbers for sequences of negatively associated and identically distributed random variables $\{X,X_n,n\ge1\}$ with general…

The classical Galton--Watson process works with a fixed probability of fission at each time step. One of the generalizations is that the probabilities depend on time. We consider one of the most complex and interesting cases when we do not…

We prove some "high probability" results on the expected value of the mean width for random perturbations of random polytopes. The random perturbations are considered for Gaussian and $p$-stable random vectors, as well as uniform…

An old conjecture states that among all simplices inscribed in the unit sphere the regular one has the maximal mean width. An equivalent formulation is that for any centered Gaussian vector $(\xi_1,\dots,\xi_n)$ satisfying $\mathbb…

The new parameterization of the generalized parton distributions t-dependence is proposed. It allows one to reproduce sufficiently well the electromagnetic form factors of the proton and neutron at small and large momentum transfer. The…

We propose a variational tail bound for norms of random vectors under moment assumptions on their one-dimensional marginals. A simplified version of the bound that parametrizes the ``aggregating distribution'' using a certain pushforward of…

We prove a pointwise version of the multi-dimensional central limit theorem for convex bodies. Namely, let X be an isotropic random vector in R^n with a log-concave density. For a typical subspace E in R^n of dimension n^c, consider the…