Related papers: Random Moment Problems under Constraints
The general notion of a stochastic ordering is that one probability distribution is smaller than a second one if the second attaches more probability to higher values than the first. Motivated by recent work on barycentric maps on spaces of…
The purpose of this paper is to study the problem of estimating a compactly supported density of probability from noisy observations of its moments. In fact, we provide a statistical approach to the famous Hausdorff classical moment…
Conditions on the generator of a Markov process to control the fluctuations of its bridges are found. In particular, continuous time random walks on graphs and gradient diffusions are considered. Under these conditions, a concentration of…
It is shown using Monte Carlo simulation that for low multiplicity events the single-event factorial moments are saturated by the statistical fluctuations. The diverse of the event-space moments $C_{p,q}$ of single-event moments with the…
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
This paper addresses the question of when projections of a high-dimensional random vector are approximately Gaussian. This problem has been studied previously in the context of high-dimensional data analysis, where the focus is on…
The aim of this note is to prove that fluctuations of uniformly random alternating sign matrices (equivalently, configurations of the six-vertex model with domain wall boundary conditions) near the boundary are described by the Gaussian…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…
We consider a general class of random matrices whose entries are centred random variables, independent up to a symmetry constraint. We establish precise high-probability bounds on the averages of arbitrary monomials in the resolvent matrix…
A well known argument in cosmology gives that the power spectrum (or structure function) $P(k)$ of mass density fluctuations produced from a uniform initial state by physics which is causal (i.e. moves matter and momentum only up to a…
We study critera for a pair $ (\{ X_n \} $, $ \{ Y_n \}) $ of approximating processes which guarantee closeness of moments by generalizing known results for the special case that $ Y_n = Y $ for all $n$ and $ X_n $ converges to $Y$ in…
Concentration of measure is a phenomenon in which a random variable that depends in a smooth way on a large number of independent random variables is essentially constant. The random variable will "concentrate" around its median or…
There are many ways of establishing upper bounds on fluctuations of random variables, but there is no systematic approach for lower bounds. As a result, lower bounds are unknown in many important problems. This paper introduces a general…
In the context of bounding probability of small deviation, there are limited general tools. However, such bounds have been widely applied in graph theory and inventory management. We introduce a common approach to substantially sharpen such…
We consider analytic continuations of Fourier transforms and Stieltjes transforms. This enables us to define what we call complex moments for some class of probability measures which do not have moments in the usual sense. There are two…
We study the non-equilibrium stationary fluctuations of a symmetric zero-range process on the discrete interval $\{1, \ldots, N-1\}$ coupled to reservoirs at sites $1$ and $N-1$, which inject and remove particles at rates proportional to…
Even though the first momenta i.e. the ensemble average quantities in canonical ensemble (CE) give the grand canonical (GC) results in large multiplicity limit, the fluctuations involving second moments do not respect this asymptotic…
We establish unconditional $\Omega$-results for all weighted even moments of primes in arithmetic progressions. We also study the moments of these moments and establish lower bounds under GRH. Finally, under GRH and LI we prove an…