Related papers: Computational Tools for the Shot Noise with Random…
We show that gamma distributions, generalized positive Linnik distributions, S2 distributions are fixed points of Poisson shot noise transforms. The corresponding response functions are identified via their inverse functions except for some…
We consider stochastically perturbed wave maps from $\mathbb{R}^{1+d}$ into $\mathbb{S}^d$, in all energy-supercritical dimensions $d \geq 3$. We show that corotational non-degenerate Gaussian additive noise leads to self-similar blowup…
We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…
Shot noise, originating from the discrete nature of electric charge, is generated by scattering processes. Shot-noise measurements have revealed microscopic charge dynamics in various quantum transport phenomena. In particular, beyond the…
We examine the statistics of current fluctuations in a junction with a quantum dot described by Kondo Hamiltonian. With the help of Keldysh technique we calculate shot noise as a function of applied voltage at zero temperature using the…
The sensitivity of gravitational-wave (GW) detectors is characterized by their noise curves, which determine the detector's reach and ability to measure the parameters of astrophysical sources accurately. The detector noise is typically…
In sequential design strategies, common in geostatistics and Bayesian optimization, the selection of a new observation point $X_{n+1}$ of a random function $\mathbf f$ is informed by past data, captured by the filtration $\mathcal…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
We consider statistical inference for a class of mixed-effects models with system noise described by a non-Gaussian integrated Ornstein-Uhlenbeck process. Under the asymptotics where the number of individuals goes to infinity with possibly…
The intensity statistics of signals in the presence of Gaussian noise is obtained by studying the model of a random signal plus a random phasor sum. The additive Gaussian noise is shown to result in a Bessel transform of the probability…
We study random Morse functions on a Riemann manifold $(M^m,g)$ defined as a random Gaussian weighted superpositions of eigenfunctions of the Laplacian of the metric $g$. The randomness is determined by a fixed Schwartz function $w$ and a…
The distribution of higher order level spacings, i.e. the distribution of $\{s_{i}^{(n)}=E_{i+n}-E_{i}\}$ with $n\geq 1$ is derived analytically using a Wigner-like surmise for Gaussian ensembles of random matrix as well as Poisson…
When random effects are correlated with sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no…
We offer theoretical and empirical insights into the impact of exogenous randomness on the effectiveness of random forests with tree-building rules independent of training data. We formally introduce the concept of exogenous randomness and…
Several proofs of the monotonicity of the non-Gaussianness (divergence with respect to a Gaussian random variable with identical second order statistics) of the sum of n independent and identically distributed (i.i.d.) random variables were…
Consider a Bernoulli-Gaussian complex $n$-vector whose components are $V_i = X_i B_i$, with $X_i \sim \Cc\Nc(0,\Pc_x)$ and binary $B_i$ mutually independent and iid across $i$. This random $q$-sparse vector is multiplied by a square random…
We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of…
We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance parameters can be finite-, high-, or infinite-dimensional. A mixture…
The problem of a linear damped noisy oscillator is treated in the presence of two multiplicative sources of noise which imply a random mass and random damping. The additive noise and the noise in the damping are responsible for an influx of…
We examine the full counting statistics of quantum dots, which display super-Poissonian shot noise. By an extension to a generic situation with many excited states we identify the underlying transport process. The statistics is a sum of…