相关论文: When Scattering Transform Meets Non-Gaussian Rando…
It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of…
We revisit the problem of Brownian diffusion with drift in order to study finite-size effects in the geometric Galton-Watson branching process. This is possible because of an exact mapping between one-dimensional random walks and geometric…
With large-scale Monte Carlo simulations, we investigate the nonsteady relaxation at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model. The dynamic scaling behavior is carefully analyzed, and the…
The significance of small-scale forcing of particles on the carrier two-dimensional turbulent flow has been shown to influence the spectral scaling properties of the carrier fluid. We investigate possible consequences of such two-way…
Fluctuations are an intrinsic feature of many-body systems, and their full statistical distributions reveal a wealth of information about the underlying physics. Of particular interest are non-Gaussian, extreme-value statistics that arise…
Second-order characteristics including covariance and spectral density functions are fundamentally important for both statistical applications and theoretical analysis in functional time series. In the high-dimensional setting where the…
We study the change in the resurgent asymptotic properties of a trans-series in two parameters, a coupling $g^2$ and a gauge index $N$, as a system passes through a large $N$ phase transition, using the universal example of the…
We investigate the continuous-variable entanglement swapping protocol in a non-Gaussian setting, with non- Gaussian states employed either as entangled inputs and/or as swapping resources. The quality of the swapping protocol is assessed in…
The scattering transform is a multilayered, wavelet-based transform initially introduced as a model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks' stability and invariance…
We show that the leading double spectral density in sum rules for Compton-like processes can be obtained by simple properties of the Borel transform, extending an approach widely used in the literature on sum rules, and known to be valid…
We consider a random process $Y(t)=\exp\{X(t)\}$, where $X(t)$ is a centered second-order process which correlation function $R(t,s)$ can be represented as $\int_{\mathbb{R}} u(t,y)\overline{u(s,y)} dy.$ A multiplicative wavelet-based…
We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of…
The scattering of coherent X-rays from dynamically evolving systems is currently becoming experimentally feasible. The scattered beam produces a pattern of bright and dark speckles, which fluctuate almost independently in time and can be…
Recent analyses of wetting in the semi-infinite two dimensional Ising model, extended to include both a surface coupling enhancement and a surface field, have shown that the wetting transition may be effectively first-order and that…
We study the second-order asymptotics of information transmission using random Gaussian codebooks and nearest neighbor (NN) decoding over a power-limited stationary memoryless additive non-Gaussian noise channel. We show that the dispersion…
From a wavelet analysis, one derives a nonparametrical estimator for the spectral density of a Gaussian process with stationary increments. First, the idealistic case of a continuous time path of the process is considered. A punctual…
We study the fluctuations of the area $A(t)= \int_0^t x(\tau)\, d\tau$ under a self-similar Gaussian process (SGP) $x(\tau)$ with Hurst exponent $H>0$ (e.g., standard or fractional Brownian motion, or the random acceleration process) that…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
This paper studies the Gaussian approximation of high-dimensional and non-degenerate U-statistics of order two under the supremum norm. We propose a two-step Gaussian approximation procedure that does not impose structural assumptions on…
We study the two-photon scattering processes in a one-dimensional waveguide coupled to a two- or three-level giant atom, respectively. The accumulated phase shift between the two coupling points can be utilized to alter the scattering…