Related papers: Locally Sampleable Uniform Symmetric Distributions
The polygonal distributions are a class of distributions that can be defined via the mixture of triangular distributions over the unit interval. The class includes the uniform and trapezoidal distributions, and is an alternative to the beta…
The distribution function of the sum of i.i.d. random variables of the special form is considered. Such sum describes messages posterior probabilities for random coding in binary symmetric channel. Close non-asymptotic lower and upper…
In this paper, we are interested in the number of fixed points of functions $f:A^n\to A^n$ over a finite alphabet $A$ defined on a given signed digraph $D$. We first use techniques from network coding to derive some lower bounds on the…
In this note we compare two measures of the complexity of a class $\mathcal F$ of Boolean functions studied in (unconditional) pseudorandomness: $\mathcal F$'s ability to distinguish between biased and uniform coins (the coin problem), and…
In this paper we prove results regarding Boolean functions with small spectral norm (the spectral norm of f is $\|\hat{f}\|_1=\sum_{\alpha}|\hat{f}(\alpha)|$). Specifically, we prove the following results for functions $f:\{0,1\}^n \to…
Suppose that $Y^n$ is obtained by observing a uniform Bernoulli random vector $X^n$ through a binary symmetric channel with crossover probability $\alpha$. The "most informative Boolean function" conjecture postulates that the maximal…
Boolean formulae compactly encode huge, constrained search spaces. Thus, variability-intensive systems are often encoded with Boolean formulae. The search space of a variability-intensive system is usually too large to explore without…
We study global distribution of zeros for a wide range of ensembles of random polynomials. Two main directions are related to almost sure limits of the zero counting measures, and to quantitative results on the expected number of zeros in…
We address a sequential decision problem that arises in the computation of symmetric Boolean functions of distributed data. We consider a collocated network, where each node's transmissions can be heard by every other node. Each node has a…
A recent discovery of Eldan and Gross states that there exists a universal $C>0$ such that for all Boolean functions $f:\{-1,1\}^n\to \{-1,1\}$, $$ \int_{\{-1,1\}^n}\sqrt{s_f(x)}d\mu(x) \ge C\text{Var}(f)\sqrt{\log…
Differential uniformity is a significant concept in cryptography as it quantifies the degree of security of S-boxes respect to differential attacks. Power functions of the form $F(x)=x^d$ with low differential uniformity have been…
For a large class of symmetric random matrices with correlated entries, selected from stationary random fields of centered and square integrable variables, we show that the limiting distribution of eigenvalue counting measure always exists…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous…
Linear network coding transmits data through networks by letting the intermediate nodes combine the messages they receive and forward the combinations towards their destinations. The solvability problem asks whether the demands of all the…
We study sequences of functions of the form F_p^n -> {0,1} for varying n, and define a notion of convergence based on the induced distributions from restricting the functions to a random affine subspace. Using a decomposition theorem and a…
In this paper, we address the scenario where nodes with sensor data are connected in a tree network, and every node wants to compute a given symmetric Boolean function of the sensor data. We first consider the problem of computing a…
We present conditions that allow us to pass from the convergence of probability measures in distribution to the uniform convergence of the associated quantile functions. Under these conditions, one can in particular pass from the asymptotic…
For fixed $t\in [0,1)$ and $h>0$, consider the local uniform empirical process $$\DD_{n,h,t}(s):=n^{-1/2}\coo\sliin 1_{[t,t+hs]}(U_i)-hs\cff,\;s\in [0,1],$$ where the $U_i$ are independent and uniformly distributed on $[0,1]$. We…
One-dimensional scattering problems are of wide physical interest and are encountered in many diverse applications. In this article I establish some very general bounds for reflection and transmission coefficients for one-dimensional…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…