Related papers: Symmetric Distributions from Shallow Circuits

Due to significant computational expense, discrete element method simulations of jammed packings of size-dispersed spheres with size ratios greater than 1:10 have remained elusive, limiting the correspondence between simulations and…

This is the first installment in a series of papers devoted to examining certain aspects of the asymptotic value distribution and distribution of zeros manifested by members of a broad class of linear combinations of L-functions in the…

The $\epsilon$-approximate degree $deg_\epsilon(f)$ of a Boolean function $f$ is the least degree of a real-valued polynomial that approximates $f$ pointwise to error $\epsilon$. The approximate degree of $f$ is at least $k$ iff there…

Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…

For a number of non-interacting identical particles entering a multi-channel scatterer in various wave packet states, we construct a generating function for the probabilities of various scattering outcomes. This is used to evaluate the mean…

Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…

We derive the explicit expression for the distribution of resonance widths in a chaotic quantum system coupled to continua via M equivalent open channels. It describes a crossover from the $\chi^2$ distribution (regime of isolated…

We discuss the asymptotic behaviour of models of lattice polygons, mainly on the square lattice. In particular, we focus on limiting area laws in the uniform perimeter ensemble where, for fixed perimeter, each polygon of a given area occurs…

It is realized that existing powerful tests of goodness-of-fit are all based on sorted uniforms and, consequently, can suffer from the confounded effect of different locations and various signal frequencies in the deviations of the…

Let $Y$ be a nonnegative random variable with mean $\mu$ and finite positive variance $\sigma^2$, and let $Y^s$, defined on the same space as $Y$, have the $Y$ size biased distribution, that is, the distribution characterized by…

With a graph $G=(V,E)$ we associate a collection of non-negative real weights $\cup_{v\in V}{\lambda_{i,v}:1\leq i \leq m} \cup \cup_{uv \in E} {\lambda_{ij,uv}:1\leq i \leq j \leq m}$. We consider the probability distribution on…

In the study of the cyclicity of a function $f$ in reproducing kernel Hilbert spaces an important role is played by sequences of polynomials $\{p_n\}_{n\in \mathbb{N}}$ called \emph{optimal polynomial approximants} (o.p.a.). For many such…

Let $f : \{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}$ be a 2-party function. For every product distribution $\mu$ on $\{0,1\}^n \times \{0,1\}^n$, we show that $$\mathsf{CC}^\mu_{0.49}(f) = O\left(\left(\log \mathsf{prt}_{1/8}(f) \cdot…

A key fact in the theory of Boolean functions $f : \{0,1\}^n \to \{0,1\}$ is that they often undergo sharp thresholds. For example: if the function $f : \{0,1\}^n \to \{0,1\}$ is monotone and symmetric under a transitive action with…

We investigate the spectral statistics of chaotic quasi one dimensional systems such as long wires. To do so we represent the spectral correlation function $R(\epsilon)$ through derivatives of a generating function and semiclassically…

We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…

In this paper we continue to study {\it quasi associated homogeneous distributions \rm{(}generalized functions\rm{)}} which were introduced in the paper by V.M. Shelkovich, Associated and quasi associated homogeneous distributions…

The problem of distributed function computation is studied, where functions to be computed is not necessarily symbol-wise. A new method to derive a converse bound for distributed computing is proposed; from the structure of functions to be…

We show that the Riemannian Gaussian distributions on symmetric spaces, introduced in recent years, are of standard random matrix type. We exploit this to compute analytically marginals of the probability density functions. This can be done…

Reflection of particles from a disordered or chaotic medium is characterized by a scattering matrix that can be represented as a superposition of resonances. Each resonance corresponds to an eigenstate inside the medium and has a width…