Related papers: Algebraic methods toward higher-order probability …

Let $\mu$ be a probability measure on $\mathbb{R}$ with cumulative distribution function $F$, $(x_{i})_{1}^{n}$ a large i.i.d. sample from $\mu$, and $F_{n}$ the associated empirical distribution function. The Glivenko-Cantelli theorem…

In [G. Kalai, A Fourier-theoretic Perspective on the Condorcet Paradox and Arrow's Theorem, Adv. in Appl. Math. 29(3) (2002), pp. 412--426], Kalai investigated the probability of a rational outcome for a generalized social welfare function…

We state and prove a generalization of Kingman's ergodic theorem on a measure-preserving dynamical system $(X,\mathcal{F},\mu,T)$ where the $\mu$-almost sure subadditivity condition $f_{n+m} \leq f_n + f_m \circ T^{n}$ is relaxed to a…

$\mu$ being a nonnegative measure satisfying some log-Sobolev inequality, we give conditions on F for the measure $\nu=e^{-2F} \mu$ to also satisfy some log-Sobolev inequality. Explicit examples are studied.

Let G be a locally compact Hausdorff group in which every element is of finite order, and let P(G) denote the class of all regular probability measures on G. In this note, it is observed that a characterization of algebraically regular…

In the first part of this two-part article, we have introduced and analyzed a multidimensional model, called the 'general tension-reduction' (GTR) model, able to describe general quantum-like measurements with an arbitrary number of…

We propose a method for inference in generalised linear mixed models (GLMMs) and several extensions of these models. First, we extend the GLMM by allowing the distribution of the random components to be non-Gaussian, that is, assuming an…

In this note, we present several inequalities in the context of pattern containment, utilizing elementary applications of the Fortuin-Kasteleyn-Ginibre (FKG) inequality and Shearer's lemma.

A representation of the perturbation series of a general functional measure is given in terms of generalized Feynman graphs and -rules. The graphical calculus is applied to certain functional measures of L\'evy type. A graphical notion of…

This paper is the first part of the series "Spherical higher order Fourier analysis over finite fields", aiming to develop the higher order Fourier analysis method along spheres over finite fields, and to solve the geometric Ramsey…

We prove a conjecture of Cuttler et al.~[2011] [A. Cuttler, C. Greene, and M. Skandera; \emph{Inequalities for symmetric means}. European J. Combinatorics, 32(2011), 745--761] on the monotonicity of \emph{normalized Schur functions} under…

Let $\mu$ be a Gaussian measure (say, on ${\bf R}^n$) and let $K, L \subset {\bf R}^n$ be such that K is convex, $L$ is a "layer" (i.e. $L = \{x : a \leq < x,u > \leq b \}$ for some $a$, $b \in {\bf R}$ and $u \in {\bf R}^n$) and the…

Given two functions $f,g:I\to\mathbf{R}$ and a probability measure $\mu$ on the Borel subsets of $[0,1]$, the two-variable mean $M_{f,g;\mu}:I^2\to I$ is defined by $$ M_{f,g;\mu}(x,y) :=\bigg(\frac{f}{g}\bigg)^{-1}\left( \frac{\int_0^1…

Recently, van den Berg and Jonasson gave the first substantial extension of the BK inequality for non-product measures: they proved that, for k-out-of-n measures, the probability that two increasing events occur disjointly is at most the…

We prove new results on common cause closedness of quantum probability spaces, where by a quantum probability space is meant the projection lattice of a non-commutative von Neumann algebra together with a countably additive probability…

In this paper, we characterize compatibility of distributions and probability measures on a measurable space. For a set of indices $\mathcal J$, we say that the tuples of probability measures $(Q_i)_{i\in \mathcal J} $ and distributions…

For $\mu$ an edge percolation measure on the infinite square lattice, let $\mu_{\textit{hp}}$ (respectively, $\mu^*_{hp}$) denote its marginal (respectively, the marginal of its planar dual process) on the upper half-plane. We show that if…

The rearrangement inequalities of Hardy-Littlewood and Riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangement. It is known that these inequalities extend to integrands…

We give an extension of the FKG inequality to the case of multiple events with equal pairwise intersections. We then apply this inequality to resolve Kahn's question on positive associated (PA) measures.

We prove a rearrangement inequality for the uncentered Hardy-Littlewood maximal function $M_{\mu}$ associate to general measure $\mu$ on $\mathbb{R}$. This inequality is analogous to the Stein's result $cf^{**}(t)\leq(Mf)^{*}(t)\leq C…