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Stochastic approximation is a powerful class of algorithms with celebrated success. However, a large body of previous analysis focuses on stochastic approximations driven by contractive operators, which is not applicable in some important…

Lower bounds for variances are often needed to derive central limit theorems. In this paper, we establish a lower bound for the variance of Poisson functionals that uses the difference operator of Malliavin calculus. Poisson functionals,…

In this paper we consider systems of weakly interacting particles driven by colored noise in a bistable potential, and we study the effect of the correlation time of the noise on the bifurcation diagram for the equilibrium states. We…

One of the most important issues in disordered systems is the interplay of the disorder and repulsive interactions. Several recent experimental advances on this topic have been made with ultracold atoms, in particular the observation of…

This work is devoted to a rigorous analysis of the weak coupling limit (WCL) for the reduced dynamics of an open infinite-dimensional quantum system interacting with electromagnetic field or a reservoir formed by Fermi or Bose particles in…

The study of quantum correlations within relativistic spacetimes, and the consequences of relativistic causality on information processing using such correlations, has gained much attention in recent years. In this paper, we establish a…

We prove clustering estimates for the truncated correlations, i.e., cumulants of an unbounded spin system on the lattice. We provide a unified treatment, based on cluster expansion techniques, of four different regimes: large mass, small…

Using cumulant expansion in Gaussian approximation, the internal quantum statistics of damped soliton-like pulses in Kerr media are studied numerically, considering both narrow and finite bandwidth spectral pulse components. It is shown…

Canonical correlation analysis investigates linear relationships between two sets of variables, but often works poorly on modern data sets due to high-dimensionality and mixed data types such as continuous, binary and zero-inflated. To…

Deep learning models are trained to minimize the error between the model's output and the actual values. The typical cost function, the Mean Squared Error (MSE), arises from maximizing the log-likelihood of additive independent, identically…

In the forthcoming large volume galaxy surveys higher order statistics will provide complementary information to the usual two point statistics. Low variance estimators of the Three Point Correlation Function (3CPF) of discrete data count…

We prove that an adequately rescaled sequence $\{F_n\}$ of self-adjoint operators, living inside a fixed free Wigner chaos of even order, converges in distribution to a centered free Poisson random variable with rate $\lambda>0$ if and only…

We present a self-contained theory for the exact calculation of particle number counting statistics of non-interacting indistinguishable particles in the canonical ensemble. This general framework introduces the concept of auxiliary…

The white noise approach to the investigation of the dynamics of a quantum particle interacting with a dilute and in general non-equilibrium gaseous environment in the low density limit is outlined. The low density limit is the kinetic…

Within a Monte Carlo simulation we investigate the statistical properties of an electron flow injected with a Poissonian distribution and transmitted under ballistic regime in the presence of long-range Coulomb interaction. Electrons are…

Multiple stochastic signals possess inherent statistical correlations, yet conventional sampling methods that process each channel independently result in data redundancy. To leverage this correlation for efficient sampling, we model…

We investigate the behavior of the residence times density function for different nonlinear dynamical systems with limit cycle behavior and perturbed parametrically with a colored noise. We present evidence that underlying the stochastic…

This paper provides refined versions of some known functional central limit theorems for conditional Poisson sampling which are more suitable for applications. The theorems presented in this paper are generalizations of some results that…

Let $P$ be a simple,stationary point process having fast decay of correlations, i.e., its correlation functions factorize up to an additive error decaying faster than any power of the separation distance. Let $P_n:= P \cap W_n$ be its…

In passive monitoring using sensor networks, low energy supplies drastically constrain sensors in terms of calculation and communication abilities. Designing processing algorithms at the sensor level that take into account these constraints…