Related papers: Non-uniform Kahn-Kalai, spread, variants, and appl…
Symmetry plays a central role in the sciences, machine learning, and statistics. For situations in which data are known to obey a symmetry, a multitude of methods that exploit symmetry have been developed. Statistical tests for the presence…
A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for…
The uncertainty principle states that a signal cannot be localized both in time and frequency. With the aim of extending this result to signals on graphs, Agaskar&Lu introduce notions of graph and spectral spreads. They show that a graph…
Exploring the graph approach, we restate the extended definition of noncontextuality provided by the contextuality-by-default framework. This extended definition avoids the assumption of nondisturbance, which states that whenever two…
We obtain quenched hitting distributions to be compound Poissonian for a certain class of random dynamical systems. The theory is general and designed to accommodate non-uniformly expanding behavior and targets that do not overlap much with…
We study structural conditions in dense graphs that guarantee the existence of vertex-spanning substructures such as Hamilton cycles. It is easy to see that every Hamiltonian graph is connected, has a perfect fractional matching and,…
A well-known conjecture of F\"uredi, Kahn, and Seymour (1993) on non-uniform hypergraph matching states that for any hypergraph with edge weights $w$, there exists a matching $M$ such that the inequality $\sum_{e\in M} g(e) w(e) \geq…
The Park-Pham theorem (previously known as the Kahn-Kalai conjecture), bounds the critical probability, $p_c(\mathcal{F})$, of the a non-trivial property $\mathcal{F}\subseteq 2^X$ that is closed under supersets by the product of a…
We derive a generalization of the Wiener-Khinchin theorem for nonstationary processes by introducing a time-dependent spectral density that is related to the time-averaged power. We use the nonstationary theorem to investigate aging…
We study the peak height distribution of certain non-stationary Gaussian random fields. The explicit peak height distribution of smooth, non-stationary Gaussian processes in 1D with general covariance is derived. The formula is determined…
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…
In this paper we propose a nonparametric graphical test based on optimal matching, for assessing the equality of multiple unknown multivariate probability distributions. Our procedure pools the data from the different classes to create a…
Given $n\in\mathbb{N}$, let $\omega\left(n\right)$ denote the number of distinct prime factors of $n$, let $Z$ denote a standard normal variable, and let $P_{n}$ denote the uniform distribution on $\left\{ 1,\ldots,n\right\} $. The…
We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every…
We establish new couplings among several random graph and multigraph models related to the random regular graph $G(n,d)$, including the configuration model and unions of random perfect matchings. As a main result, we verify the…
We study mixture of linear regression (random coefficient) models, which capture population heterogeneity by allowing the regression coefficients to follow an unknown distribution $G^*$. In contrast to common parametric methods that fix the…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
We investigate the effects of non-commutative geometry on the topological aspects of gauge theory using a non-perturbative formulation based on the twisted reduced model. The configuration space is decomposed into topological sectors…
We propose a novel nonparametric approach for estimating the location of block boundaries (change-points) of non-overlapping blocks in a random symmetric matrix which consists of random variables having their distribution changing from one…
Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or regularity) and expanding the breadth of its…