Related papers: 0--1 laws for regular conditional distributions

We show that under minimal assumptions on a class of functions $\mathcal{H}$ defined on a probability space $(\mathcal{X},\mu)$, there is a threshold $\Delta_0$ satisfying the following: for every $\Delta\geq\Delta_0$, with probability at…

We give conditions under which a sequence of randomly chosen orthogonal subspaces of a separable Hilbert space generates the whole space.

The celebrated theorem of Komlos asserts that L1-boundedness is sufficient for a given sequence of functions to contain a subsequence along which (in a "lacunary" manner), and along whose every further subsequence ("hereditarily"), a strong…

Some sufficient conditions on a simplicial space $X$ guaranteeing that $X_1\simeq \Omega|X|$ were given by Segal. We give a generalization of this result for multisimplicial spaces. This generalization is appropriate for the reduced bar…

We give a framework for dealing with 0-1 laws (for first order logic) such that expanding by further random structure tend to give us another case of the framework. From another perspective we deal with 0-1 laws when the number of solutions…

It is known that real Non-Gaussian stable distributions are unimodal, not additive strongly unimodal, and multiplicative strongly unimodal in the symmetric case. By a theorem of Cuculescu-Theodorescu, the only remaining relevant situation…

In the unit ball B(0,1), let $u$ and $\Omega$ (a domain in $\R$) solve the following overdetermined problem: $$\Delta u =\chi_\Omega\quad \hbox{in} B(0,1), \qquad 0 \in \partial \Omega, \qquad u=|\nabla u |=0 \quad \hbox{in} B(0,1)\setminus…

This paper has been withdrawn. This paper focuses on the admissibility condition for fractional-order singular system with order $\alpha \in (0,1)$. The definitions of regularity, impulse-free and admissibility are given first, then a…

Shelah Spencer [ShSp:304] proved the 0-1 law for the random graphs G(n,p_n), p_n=n^{- alpha}, alpha in (0,1) irrational (set of nodes in [n]= {1, ...,n}, the edges are drawn independently, probability of edge is p_n). One may wonder what…

In this paper, we have considered a uniform distribution on a regular polygon with $k$-sides for some $k\geq 3$ and the set of all its $k$ vertices as a conditional set. For the uniform distribution under the conditional set first, for all…

Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what…

Let $k$ be a perfect complete valued field with a nontrivial non-archimedean norm $|\cdot|$ and $\omega\in k$ with $0<|\omega|<1.$ Let $X$ be a reduced and normal $k$-analytic space. Then $O^{\circ}\simeq…

Under some mild regularity on the normalizing sequence, we obtain necessary and sufficient conditions for the Strong Law of Large Numbers for (symmetrized) U-statistics. We also obtain nasc's for the a.s. convergence of series of an…

We study the approximation properties of a harmonic function $u \in H\sp{1-k}(\Omega)$, $k > 0$, on relatively compact sub-domain $A$ of $\Omega$, using the Generalized Finite Element Method. For smooth, bounded domains $\Omega$, we obtain…

We consider the equation $\e^{2}\Delta u=(u-a(x))(u^2-1)$ in $\Omega$, $\frac{\partial u}{\partial \nu} =0$ on $\partial \Omega$, where $\Omega$ is a smooth and bounded domain in $\R^n$, $\nu$ the outer unit normal to $\pa\Omega$, and $a$ a…

The need to condition distributional properties such as expectation, variance, and entropy arises in algorithmic fairness, model simplification, robustness and many other areas. At face value however, distributional properties are not…

We study the conditional distribution of zeros of a Gaussian system of random polynomials (and more generally, holomorphic sections), given that the polynomials or sections vanish at a point p (or a fixed finite set of points). The…

By making use of arithmetic information inequalities, we give a strong quantitative bound for the discretised ring theorem. In particular, we show that if $A \subset [1,2]$ is a $(\delta,\sigma)$-set, with $|A| = \delta^{-\sigma},$ then…

Let $\mathcal G$ denote the space of finitely generated marked groups. We give equivalent characterizations of closed subspaces $\mathcal S\subseteq \mathcal G$ satisfying the following zero-one law: for any sentence $\sigma$ in the…

Let $\alpha \in (0,1)_{\mathbb{R}}$ be irrational and $G_n = G_{n,1/n^\alpha}$ be the random graph with edge probability $1/n^\alpha$; we know that it satisfies the 0-1 law for first order logic. We deal with the failure of the 0-1 law for…