Related papers: Central and Non-central Limit Theorems arising fro…

It is a common assumption that the activation of different layers in neural networks follow Gaussian distribution. This distribution can be transformed using normalization techniques, such as batch-normalization, increasing convergence…

In this paper, we establish the Central Limit Theorem (CLT) for linear spectral statistics (LSSs) of large-dimensional generalized spiked sample covariance matrices, where the spiked eigenvalues may be either bounded or diverge to infinity.…

Nonanalytic features are interesting in physics as they carry valuable information about the physical properties of the system. These properties manifest themselves in observables containing a one- or two-particle spectral function. In this…

General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…

One of the characteristic features of a stochastic process under resetting is that the probability density converges to a nonequilibrium stationary state (NESS). In addition, the approach to the stationary state exhibits a dynamical phase…

We establish central limit theorems (CLTs) for the linear spectral statistics of the adjacency matrix of inhomogeneous random graphs across all sparsity regimes, providing explicit covariance formulas under the assumption that the variance…

Most chemical processes, such as distillation, absorption, extraction, and catalytic reactions, are extremely complex processes that are affected by multiple factors. The relationships between their input variables and output variables are…

Filtered shot noise processes have proven to be very effective in modelling the evolution of systems exposed to stochastic shot noise sources, and have been applied to a wide variety of fields ranging from electronics through biology. In…

Spiking Neural Networks (SNNs) have emerged as an attractive spatio-temporal computing paradigm for complex vision tasks. However, most existing works yield models that require many time steps and do not leverage the inherent temporal…

The multiple scattering theory (MST) is a Green's function method that has been widely used in electronic structure calculations for crystalline disordered systems. The key property of the MST method is the scattering path matrix (SPM) that…

We develop a new toolbox for the analysis of the global behavior of stochastic discrete particle systems. We introduce and study the notion of the Schur generating function of a random discrete configuration. Our main result provides a…

A satisfactory understanding of information processing in spiking neural networks requires appropriate computational abstractions of neural activity. Traditionally, the neural population state vector has been the most common abstraction…

Recent work in dynamic causal inference introduced a class of discrete-time stochastic processes that generalize martingale difference sequences and arrays as follows: the random variates in each sequence have expectation zero given certain…

This paper develops central limit theorems (CLT's) and large deviations results for additive functionals associated with reflecting diffusions in which the functional may include a term associated with the cumulative amount of boundary…

Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLT's) for linear spectral statistics of high-dimensional non-centered sample covariance matrices have received considerable…

The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be…

Recent neuroimaging studies have highlighted the importance of network-centric brain analysis, particularly with functional magnetic resonance imaging. The emergence of Deep Neural Networks has fostered a substantial interest in predicting…

We consider sequences of needlet random fields defined as weighted averaged forms of spherical Gaussian eigenfunctions. Our main result is a Central Limit Theorem in the high energy setting, for the boundary lengths of their excursion sets.…

The characterization of neural responses to sensory stimuli is a central problem in neuroscience. Spike-triggered average (STA), an influential technique, has been used to extract optimal linear kernels in a variety of animal subjects.…

The landscape of deep learning has vastly expanded the frontiers of source code analysis, particularly through the utilization of structural representations such as Abstract Syntax Trees (ASTs). While these methodologies have demonstrated…