Related papers: Conditional distribution of the sample mean and lo…
We show that the hypothesis of regularity of the conditional distribution of the empiric average of a finite sample of IID random variables, given all the sample "fluctuations", which appeared in our earlier manuscript |1] in the context of…
We give an improved estimate for the regularity of the conditional distribution of the empiric mean of a finite sample of IID random variables, conditional on the sample "fluctuations", extending the well-known property of Gaussian IID…
We use a new eigenvalue concentration bound for the fluctuation of the sample mean of the random extternal potential in the multi-particle Anderson model and prove the spectral exponential and the strong dynamical localization. The results…
We report on recent results on the spectral statistics of the discrete Anderson model in the localized phase. Our results show, in particular, that, for the discrete Anderson Hamiltonian with smoothly distributed random potential at…
A stochastic model for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas has been constructed based on a super-position of uncorrelated pulses arriving according to a Poisson process. In the most common…
In this paper, we examine fluctuations of polynomial linear statistics for the Anderson model on $\mathbb{Z}^d$ for any potential with finite moments. We prove that if normalized by the square root of the size of the truncated operator,…
We demonstrate the presence of energy dependent fluctuations in the localization length, which depend on the disorder distribution. These fluctuations lead to Ensemble Averaged Conductance Fluctuations (EACF) and are enhanced by large…
We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…
We extend to Gaussian distributions a result providing smoothed analysis estimates for condition numbers given as relativized distances to illposedness. We also introduce a notion of local analysis meant to capture the behavior of these…
We propose and analyze a generalized splitting method to sample approximately from a distribution conditional on the occurrence of a rare event. This has important applications in a variety of contexts in operations research, engineering,…
In this paper, we consider a property of univariate Gaussian distributions namely conditional expectation shift (or centroid shift). Specifically, we compare two Gaussian distributions in which they differ only in their means. Equivalently,…
Consider the parabolic Anderson model $\partial_tu=\frac{1}{2}\partial_x^2u+u\, \eta$ on the interval $[0, L]$ with Neumann, Dirichlet or periodic boundary conditions, driven by space-time white noise $\eta$. Using Malliavin-Stein method,…
We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of…
We consider the classical problem of discrete distribution estimation using i.i.d. samples in a novel scenario where additional side information is available on the distribution. In large alphabet datasets such as text corpora, such side…
We study spectra and localization properties of Euclidean random matrices. The problem is approximately mapped onto that of a matrix defined on a random graph. We introduce a powerful method to find the density of states and the…
For the multi-particle Anderson model with correlated random potential in the continuum, we show under fairly general assumptions on the inter-particle interaction and the random external potential, the Anderson localization which consists…
We explore some properties of the conditional distribution of an i.i.d. sample under large exceedances of its sum. Thresholds for the asymptotic independance of the summands are observed, in contrast with the classical case when the…
Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling…
We reconcile the phenomenon of mesoscopic conductance fluctuations with the single parameter scaling theory of the Anderson transition. We calculate three averages of the conductance distribution: $\exp(<\ln g>)$, $<g>$ and $1/<R>$ where…
Following [5], we analyze regularity properties of single-site probability distributions of the random potential and of the Integrated Density of States (IDS) in the Anderson models with infinite-range interactions. In the present work, we…