相关论文: When Scattering Transform Meets Non-Gaussian Rando…
Large deviation principles are established for the two-parameter Poisson-Dirichlet distribution and two-parameter Dirichlet process when parameter $\theta$ approaches infinity. The motivation for these results is to understand the…
We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit…
We study mean-field inclusion processes with an additional slow phase, in which particle interactions occur at a vanishing rate proportional to the inverse system size. In the thermodynamic limit, such systems exhibit condensation at high…
We discuss the limiting spectral density of real symmetric random matrices. Other than in standard random matrix theory the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic…
A Galton-Watson process in varying environment is a discrete time branching process where the offspring distributions vary among generations. Based on a two-spine decomposition technique, we provide a probabilistic argument of a Yaglom-type…
We study fluctuations of the empirical processes of a non-equilibrium interacting particle system consisting of two species over a domain that is recently introduced in [8] and establish its functional central limit theorem. This…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
We show the potential for classifying images of mixtures of aggregate, based themselves on varying, albeit well-defined, sizes and shapes, in order to provide a far more effective approach compared to the classification of individual sizes…
The asymptotic mutual information (MI) analysis for multiple-input multiple-output (MIMO) systems over double-scattering channels has achieved engaging results, but the convergence rates of the mean, variance, and the distribution of the MI…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
We consider whether the non-Gaussian scale-dependent halo bias can be used not only to constrain the local form of non-Gaussianity but also to distinguish among different shapes. In particular, we ask whether it can constrain the behavior…
We consider a non-Gaussian stochastic process where a particle diffuses in the $y$-direction, $dy/dt=\eta(t)$, subject to a transverse shear flow in the $x$-direction, $dx/dt=f(y)$. Absorption with probability $p$ occurs at each crossing of…
Scattering hinders the passage of light through random media and consequently limits the usefulness of optical techniques for sensing and imaging. Thus, methods for increasing the transmission of light through such random media are of…
We propose a new approach to supercontinuum generation and carrier-envelope-offset detection based on saturated second-order nonlinear interactions in dispersion-engineered nanowaveguides. The technique developed here broadens the…
A properly scaled critical Galton-Watson process converges to a continuous state critical branching process $\xi(\cdot)$ as the number of initial individuals tends to infinity. We extend this classical result by allowing for overlapping…
The derivation of a quantum Markovian model for an opto-mechanical system consisting of a quantum mechanical mirror interacting with quantum optical input fields via radiation pressure is difficult problem which ultimately involves the…
We present the generalization of the two-dimensional quantum scattering formalism to systems with Rashba spin-orbit coupling. Using symmetry considerations, we show that the differential scattering cross section depends on the spin state of…
The first passage time process of a L\'evy subordinator with heavy-tailed L\'evy measure has long-range dependent paths. The random fluctuations that appear under two natural schemes of summation and time scaling of such stochastic…
We consider the long-time behavior of a diffusion process on $\mathbb{R}^d$ advected by a stationary random vector field which is assumed to be divergence-free, dihedrally symmetric in law and have a log-correlated potential. A special case…
We consider the evolution of self-gravitating matter fields that may undergo phase transitions, and we connect ideas from phase transition dynamics with concepts from bouncing cosmology. Our framework introduces scattering maps prescribed…