相关论文: Limit laws for boolean convolutions
We study functional limit theorems for linear type processes with short memory under the assumption that the innovations are dependent identically distributed random variables with infinite variance and in the domain of attraction of stable…
This article investigates general scaling settings and limit distributions of functionals of filtered random fields. The filters are defined by the convolution of non-random kernels with functions of Gaussian random fields. The case of…
We obtain limit theorems for the row extrema of a triangular array of zero-modified geometric random variables. Some of this is used to obtain limit theorems for the maximum family size within a generation of a simple branching process with…
Let $\{V_{i,j}; (i,j)\in\N^2\}$ be a two-dimensional array of i.i.d.\ random variables. The limit laws of the sum of independent random products $$ Z_n=\sum_{i=1}^{N_n} \prod_{j=1}^{n} e^{V_{i,j}} $$ as $n,N_n\to\infty$ have been…
Many mathematical, man-made and natural systems exhibit a leading-digit bias, where a first digit (base 10) of 1 occurs not 11\% of the time, as one would expect if all digits were equally likely, but rather 30\%. This phenomenon is known…
We study the Coulomb chain where particles are restricted to one dimension and experience three-dimensional Coulomb interactions with their nearest and next-to-nearest neighbours. The distances between consecutive particles are treated as…
We analyse the limiting behavior of the eigenvalue and singular value distribution for random convolution operators on large (not necessarily Abelian) groups, extending the results by M. Meckes for the Abelian case. We show that for regular…
We study sequences of functions of the form F_p^n -> {0,1} for varying n, and define a notion of convergence based on the induced distributions from restricting the functions to a random affine subspace. Using a decomposition theorem and a…
Instrumental variables have proven useful, in particular within the social sciences and economics, for making inference about the causal effect of a random variable, B, on another random variable, C, in the presence of unobserved…
We obtain the analogue of the classical result by Erd\"os and Kac on the limiting distribution of the maximum of partial sums for exchangeable random variables with zero mean and variance one. We show that, if the conditions of the central…
Free probability analogs of the basics of extreme-value theory are obtained, based on Ando's spectral order. This includes classification of freely max-stable laws and their domains of attraction, using ``free extremal convolutions'' on the…
Limit theorems of strong law of large numbers and central limit theorem types are obtained for the compositions of independent identically distributed random unitary channels.
We report on recent progress in the study of evolution processes involving degenerate parabolic equations what may exhibit free boundaries. The equations we have selected follow to recent trends in diffusion theory: considering anomalous…
The phenomenon of superconvergence is proved for all freely infinitely divisible distributions. Precisely, suppose that the partial sums of a sequence of free identically distributed, infinitesimal random variables converge in distribution…
Using sum rules and a new dipole-free sum-over-states expression, we calculate the fundamental limits of the dispersion of the real and imaginary parts of all electronic nonlinear-optical susceptibilities. As such, these general results can…
Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained. The results apply to general Gaussian processes including fractional Brownian motion, sub-fractional Brownian motion and…
We prove that the distribution of the product of two correlated normal random variables with arbitrary means and arbitrary variances is infinitely divisible. We also obtain exact formulas for the probability density function of the sum of…
We consider a limit theorem for a triangular array of point processes generated by non-identically distributed random variables, and apply the result for the analysis of the limiting behavior of the Argmaximum of independent random…
We introduce a new natural notion of convergence for permutations at any specified scale, in terms of the density of patterns of restricted width. In this setting we prove that limits may be chosen independently at a countably infinite…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…