A Local Limit Theorem on the Semi-Direct Product of $\mathbb {R}^{*+}$ and $\mathbb {R}^d$

Emile Le Page; Marc Peigne

Displaying similar documents to “A Local Limit Theorem on the Semi-Direct Product of $ℝ^{* +}$ and $ℝ^{d}$ ”

On $(n, m)$ - $A$ -normal and $(n, m)$ - $A$ -quasinormal semi-Hilbertian space operators

Samir Al Mohammady, Sid Ahmed Ould Beinane, Sid Ahmed Ould Ahmed Mahmoud (2022)

Mathematica Bohemica

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The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces, i.e. spaces generated by positive semi-definite sesquilinear forms. Let $ℋ$ be a Hilbert space and let $A$ be a positive bounded operator on $ℋ$ . The semi-inner product ${〈 h ∣ k 〉}_{A} : = 〈 A h ∣ k 〉$ , $h, k \in ℋ$ , induces a semi-norm ${∥ \cdot ∥}_{A}$ . This makes $ℋ$ into a semi-Hilbertian space. An operator $T \in ℬ_{A} (ℋ)$ is said to be $(n, m)$ - $A$ -normal if $[T^{n}, {(T^{♯_{A}})}^{m}] : = T^{n} {(T^{♯_{A}})}^{m} - {(T^{♯_{A}})}^{m} T^{n} = 0$ for some positive integers $n$ and $m$ .

Some properties of the topology of $α$ -sets

D. Andrijević (1984)

Matematički Vesnik

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Spaces of functions on domain $Ω$ , whose $k$ -th derivatives are measures defined on $\bar{Ω}$

Jiří Souček (1972)

Časopis pro pěstování matematiky

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Some results on semi-stratifiable spaces

Wei-Feng Xuan, Yan-Kui Song (2019)

Mathematica Bohemica

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We study relationships between separability with other properties in semi-stratifiable spaces. Especially, we prove the following statements: (1) If $X$ is a semi-stratifiable space, then $X$ is separable if and only if $X$ is $D C (ω_{1})$ ; (2) If $X$ is a star countable extent semi-stratifiable space and has a dense metrizable subspace, then $X$ is separable; (3) Let $X$ be a $ω$ -monolithic star countable extent semi-stratifiable space. If $t (X) = ω$ and $d (X) \leq ω_{1}$ , then $X$ is hereditarily separable. Finally, we prove that for...

Migrativity properties of 2-uninorms over semi-t-operators

Ying Li-Jun, Qin Feng (2022)

Kybernetika

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In this paper, we analyze and characterize all solutions about $α$ -migrativity properties of the five subclasses of 2-uninorms, i. e. $C^{k}$ , $C_{k}^{0}$ , $C_{k}^{1}$ , $C_{1}^{0}$ , $C_{0}^{1}$ , over semi-t-operators. We give the sufficient and necessary conditions that make these $α$ -migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for $G \in C^{k}$ , the $α$ -migrativity of $G$ over a semi-t-operator $F_{μ, ν}$ is closely related to the $α$ -section of $F_{μ, ν}$ or the ordinal sum representation...

Soft local times and decoupling of random interlacements

Serguei Popov, Augusto Teixeira (2015)

Journal of the European Mathematical Society

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In this paper we establish a decoupling feature of the random interlacement process $ℐ^{u} \subset ℤ^{d}$ at level $u$ , $d \geq 3$ . Roughly speaking, we show that observations of $ℐ^{u}$ restricted to two disjoint subsets $A_{1}$ and $A_{2}$ of $ℤ^{d}$ are approximately independent, once we add a sprinkling to the process $ℐ^{u}$ by slightly increasing the parameter $u$ . Our results differ from previous ones in that we allow the mutual distance between the sets $A_{1}$ and $A_{2}$ to be much smaller than their diameters. We then provide an important application...

Positivity of integrated random walks

Vladislav Vysotsky (2014)

Annales de l'I.H.P. Probabilités et statistiques

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Take a centered random walk $S_{n}$ and consider the sequence of its partial sums $A_{n} : = \sum_{i = 1}^{n} S_{i}$ . Suppose $S_{1}$ is in the domain of normal attraction of an $α$ -stable law with $1 l t; α \leq 2$ . Assuming that $S_{1}$ is either right-exponential (i.e. $ℙ (S_{1} g t; x | S_{1} g t; 0) = e^{- a x}$ for some $a g t; 0$ and all $x g t; 0$ ) or right-continuous (skip free), we prove that $ℙ {A_{1} g t; 0, \dots, A_{N} g t; 0} \sim C_{α} N^{1 / (2 α) - 1 / 2}$ as $N \to \infty$ , where $C_{α} g t; 0$ depends on the distribution of the walk. We also consider a conditional version of this problem and study positivity of integrated discrete bridges.

La Queste del Saint $G R_{a}$ (AL): a Computational Approach to Local Algebra

Teo Mora (1989)

Publications mathématiques et informatique de Rennes

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Random ε-nets and embeddings in $ℓ_{\infty}^{N}$

Y. Gordon, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann (2007)

Studia Mathematica

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We show that, given an n-dimensional normed space X, a sequence of $N = {(8 / ε)}^{2 n}$ independent random vectors ${(X_{i})}_{i = 1}^{N}$ , uniformly distributed in the unit ball of X*, with high probability forms an ε-net for this unit ball. Thus the random linear map $Γ : ℝ \to ℝ^{N}$ defined by $Γ x = {(⟨ x, X_{i} ⟩)}_{i = 1}^{N}$ embeds X in $ℓ_{\infty}^{N}$ with at most 1 + ε norm distortion. In the case X = ℓ₂ⁿ we obtain a random 1+ε-embedding into $ℓ_{\infty}^{N}$ with asymptotically best possible relation between N, n, and ε.

Some limit theorems for $m$ -pairwise negative quadrant dependent random variables

Yongfeng Wu, Jiangyan Peng (2018)

Kybernetika

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The authors first establish the Marcinkiewicz-Zygmund inequalities with exponent $p$ ( $1 \leq p \leq 2$ ) for $m$ -pairwise negatively quadrant dependent ( $m$ -PNQD) random variables. By means of the inequalities, the authors obtain some limit theorems for arrays of rowwise $m$ -PNQD random variables, which extend and improve the corresponding results in [Y. Meng and Z. Lin (2009)] and [H. S. Sung (2013)]. It is worthy to point out that the open problem of [H. S. Sung, S. Lisawadi, and A. Volodin (2008)] can be...

Asymptotic behavior of a stochastic combustion growth process

Alejandro Ramírez, Vladas Sidoravicius (2004)

Journal of the European Mathematical Society

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We study a continuous time growth process on the $d$ -dimensional hypercubic lattice $𝒵^{d}$ , which admits a phenomenological interpretation as the combustion reaction $A + B \to 2 A$ , where $A$ represents heat particles and $B$ inert particles. This process can be described as an interacting particle system in the following way: at time 0 a simple symmetric continuous time random walk of total jump rate one begins to move from the origin of the hypercubic lattice; then, as soon as any random walk visits a site...

Localization techniques in $L^{p}$ spaces

A. Pełczyński, H. Rosenthal (1975)

Studia Mathematica

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Extremally disconnected resolutions of $T_{0}$ -spaces

A. Błaszczyk (1974)

Colloquium Mathematicae

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On the equation $ϕ (x + m) = ϕ (x) + m$

A. Makowski (1964)

Matematički Vesnik

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Multi-variate correlation and mixtures of product measures

Tim Austin (2020)

Kybernetika

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Total correlation (‘TC’) and dual total correlation (‘DTC’) are two classical ways to quantify the correlation among an $n$ -tuple of random variables. They both reduce to mutual information when $n = 2$ . The first part of this paper sets up the theory of TC and DTC for general random variables, not necessarily finite-valued. This generality has not been exposed in the literature before. The second part considers the structural implications when a joint distribution $μ$ has small TC or DTC. If...

On the proximate order of $f^{(s)} (z) * g^{(s)} (z)$ and ${[f (z) * g (z)]}^{(s)}$

M. K. Sen (1971)

Annales Polonici Mathematici

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Геометрическая теория состояний, граница фон Неймана, двойственность $C^{*}$ -алгерб

А.М. Вершик (1972)

Zapiski naucnych seminarov Leningradskogo

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Displaying similar documents to “A Local Limit Theorem on the Semi-Direct Product of ℝ * + and ℝ d ”

Displaying similar documents to “A Local Limit Theorem on the Semi-Direct Product of $ℝ^{* +}$ and $ℝ^{d}$ ”