Related papers: Density and Distribution Evaluation for Convolutio…
For random piecewise linear systems T of the interval that are expanding on average we construct explicitly the density functions of absolutely continuous T-invariant measures. In case the random system uses only expanding maps our…
We analyze the time reversed dynamics of generative diffusion models. If the exact empirical score function is used in a regime of large dimension and exponentially large number of samples, these models are known to undergo transitions…
We establish a comprehensive probability theory for coherent transport of random waves through arbitrary linear media. The transmissivity distribution for random coherent waves is a fundamental B-spline with knots at the transmission…
We present an invariant density for the finite Gauss transformation of the unit interval and discuss some properties of this transformation.
Density ratio estimation in high dimensions can be reframed as integrating a certain quantity, the time score, over probability paths which interpolate between the two densities. In practice, the time score has to be estimated based on…
We consider nonparametric measurement error density deconvolution subject to heteroscedastic measurement errors as well as symmetry about zero and shape constraints, in particular unimodality. The problem is motivated by applications where…
We apply random matrix theory to study the impact of measurement uncertainty on dynamic mode decomposition. Specifically, when the measurements follow a normal probability density function, we show how the moments of that density propagate…
This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be…
Generative diffusion processes are an emerging and effective tool for image and speech generation. In the existing methods, the underline noise distribution of the diffusion process is Gaussian noise. However, fitting distributions with…
The exponential sensitivity of cluster number counts to the properties of the dark energy implies a comparable sensitivity to not only the mean but also the actual_distribution_ of an observable mass proxy given the true cluster mass. For…
In some applications it is necessary to estimate derivatives of probability densities defined on the positive semi-axis. The quality of nonparametric estimates of the probability densities and their derivatives are strongly influenced by…
In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of…
Linear combinations of chi square random variables occur in a wide range of fields. Unfortunately, a closed, analytic expression for the pdf is not yet known. As a first result of this work, an explicit analytic expression for the density…
The relationship between the spectral density and free energy of a spin system is considered. The analytical expressions allowing for the calculation of the spectral density for solvable models are determined. A linear Ising model is taken…
This work proposes algorithms for computing additive and multiplicative free convolutions of two given measures. We consider measures with compact support whose free convolution results in a measure with a density function that exhibits a…
This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the…
Response calculations in density functional theory aim at computing the change in ground-state density induced by an external perturbation. At finite temperature these are usually performed by computing variations of orbitals, which involve…
We consider the problem of multivariate density deconvolution when the interest lies in estimating the distribution of a vector-valued random variable but precise measurements of the variable of interest are not available, observations…
Let $X,X_1,\ldots,X_n$ be independent identically distributed random variables. The paper deals with the question about the behavior of the concentration function of the random variable $\sum\limits_{k=1}^{n}X_k a_k$ according to the…
Granular segregation is ubiquitous in industrial, geological or daily-life context, but there is still no unifying theoretical approach. In this review, we examine two examples of granular segregation -- shallow rapid flows and rotating…