Displaying similar documents to “Corrigenda to “Operator semi-stable probability measures on R N ””

On the powers of Voiculescu's circular element

Ferenc Oravecz (2001)

Studia Mathematica

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The main result of the paper is that for a circular element c in a C*-probability space, ( c , c n * ) is an R-diagonal pair in the sense of Nica and Speicher for every n = 1,2,... The coefficients of the R-series are found to be the generalized Catalan numbers of parameter n-1.

Limit theorems for random fields

Nguyen van Thu

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CONTENTSIntroduction............................................................................................................................................................................ 51. Notation and preliminaries............................................................................................................................................ 52. Statement of the problem..................................................................................................................................................

On the isotropic constant of marginals

Grigoris Paouris (2012)

Studia Mathematica

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We show that if μ₁, ..., μₘ are log-concave subgaussian or supergaussian probability measures in n i , i ≤ m, then for every F in the Grassmannian G N , n , where N = n₁ + ⋯ + nₘ and n< N, the isotropic constant of the marginal of the product of these measures, π F ( μ μ ) , is bounded. This extends known results on bounds of the isotropic constant to a larger class of measures.

On inhomogeneous self-similar measures and their L q spectra

Przemysław Liszka (2013)

Annales Polonici Mathematici

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Let S i : d d for i = 1,..., N be contracting similarities, let ( p , . . . , p N , p ) be a probability vector and let ν be a probability measure on d with compact support. It is well known that there exists a unique inhomogeneous self-similar probability measure μ on d such that μ = i = 1 N p i μ S i - 1 + p ν . We give satisfactory estimates for the lower and upper bounds of the L q spectra of inhomogeneous self-similar measures. The case in which there are a countable number of contracting similarities and probabilities is considered. In particular,...

On the duality between p -modulus and probability measures

Luigi Ambrosio, Simone Di Marino, Giuseppe Savaré (2015)

Journal of the European Mathematical Society

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Motivated by recent developments on calculus in metric measure spaces ( X , d , m ) , we prove a general duality principle between Fuglede’s notion [15] of p -modulus for families of finite Borel measures in ( X , d ) and probability measures with barycenter in L q ( X , m ) , with q dual exponent of p ( 1 , ) . We apply this general duality principle to study null sets for families of parametric and non-parametric curves in X . In the final part of the paper we provide a new proof, independent of optimal transportation, of the...

Wasserstein metric and subordination

Philippe Clément, Wolfgang Desch (2008)

Studia Mathematica

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Let ( X , d X ) , ( Ω , d Ω ) be complete separable metric spaces. Denote by (X) the space of probability measures on X, by W p the p-Wasserstein metric with some p ∈ [1,∞), and by p ( X ) the space of probability measures on X with finite Wasserstein distance from any point measure. Let f : Ω p ( X ) , ω f ω , be a Borel map such that f is a contraction from ( Ω , d Ω ) into ( p ( X ) , W p ) . Let ν₁,ν₂ be probability measures on Ω with W p ( ν , ν ) finite. On X we consider the subordinated measures μ i = Ω f ω d ν i ( ω ) . Then W p ( μ , μ ) W p ( ν , ν ) . As an application we show that the solution measures ϱ α ( t ) ...

On nearly radial marginals of high-dimensional probability measures

Bo&#039;az Klartag (2010)

Journal of the European Mathematical Society

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Suppose that μ is an absolutely continuous probability measure on R n, for large n . Then μ has low-dimensional marginals that are approximately spherically-symmetric. More precisely, if n ( C / ε ) C d , then there exist d -dimensional marginals of μ that are ε -far from being sphericallysymmetric, in an appropriate sense. Here C > 0 is a universal constant.

Stable solutions of Δ u = f ( u ) in N

Louis Dupaigne, Alberto Farina (2010)

Journal of the European Mathematical Society

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Several Liouville-type theorems are presented for stable solutions of the equation - Δ u = f ( u ) in N , where f > 0 is a general convex, nondecreasing function. Extensions to solutions which are merely stable outside a compact set are discussed.

A descent map for curves with totally degenerate semi-stable reduction

Shahed Sharif (2013)

Journal de Théorie des Nombres de Bordeaux

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Let K be a local field of residue characteristic p . Let C be a curve over K whose minimal proper regular model has totally degenerate semi-stable reduction. Under certain hypotheses, we compute the prime-to- p rational torsion subgroup on the Jacobian of C . We also determine divisibility of line bundles on C , including rationality of theta characteristics and higher spin structures. These computations utilize arithmetic on the special fiber of C .

A characterization of partition polynomials and good Bernoulli trial measures in many symbols

Andrew Yingst (2014)

Colloquium Mathematicae

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Consider an experiment with d+1 possible outcomes, d of which occur with probabilities x , . . . , x d . If we consider a large number of independent occurrences of this experiment, the probability of any event in the resulting space is a polynomial in x , . . . , x d . We characterize those polynomials which arise as the probability of such an event. We use this to characterize those x⃗ for which the measure resulting from an infinite sequence of such trials is good in the sense of Akin.

Osgood type conditions for an m th-order differential equation

Stanisaw Szufla (1998)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We present a new theorem on the differential inequality u ( m ) w ( u ) . Next, we apply this result to obtain existence theorems for the equation x ( m ) = f ( t , x ) .

Continuous linear functionals on the space of Borel vector measures

Pola Siwek (2008)

Annales Polonici Mathematici

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We study properties of the space ℳ of Borel vector measures on a compact metric space X, taking values in a Banach space E. The space ℳ is equipped with the Fortet-Mourier norm | | · | | and the semivariation norm ||·||(X). The integral introduced by K. Baron and A. Lasota plays the most important role in the paper. Investigating its properties one can prove that in most cases the space ( , | | · | | ) * is contained in but not equal to the space (ℳ,||·||(X))*. We obtain a representation of the continuous functionals...

On NIP and invariant measures

Ehud Hrushovski, Anand Pillay (2011)

Journal of the European Mathematical Society

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We study forking, Lascar strong types, Keisler measures and definable groups, under an assumption of NIP (not the independence property), continuing aspects of the paper [16]. Among key results are (i) if p = tp ( b / A ) does not fork over A then the Lascar strong type of b over A coincides with the compact strong type of b over A and any global nonforking extension of p is Borel definable over bdd ( A ) , (ii) analogous statements for Keisler measures and definable groups, including the fact that G 000 = G 00 for G ...

Integral representation and relaxation for functionals defined on measures

Ennio De Giorgi, Luigi Ambrosio, Giuseppe Buttazzo (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Given a separable metric locally compact space Ω , and a positive finite non-atomic measure λ on Ω , we study the integral representation on the space of measures with bounded variation Ω of the lower semicontinuous envelope of the functional F ( u ) = Ω f ( x , u ) 𝑑 λ    u L 1 ( Ω , λ , n ) with respect to the weak convergence of measures.

Convergence to stable laws and a local limit theorem for stochastic recursions

Mariusz Mirek (2010)

Colloquium Mathematicae

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We consider the random recursion X x = M X n - 1 x + Q + N ( X n - 1 x ) , where x ∈ ℝ and (Mₙ,Qₙ,Nₙ) are i.i.d., Qₙ has a heavy tail with exponent α > 0, the tail of Mₙ is lighter and N ( X n - 1 x ) is smaller at infinity, than M X n - 1 x . Using the asymptotics of the stationary solutions we show that properly normalized Birkhoff sums S x = k = 0 n X k x converge weakly to an α-stable law for α ∈ (0,2]. The related local limit theorem is also proved.

Order relations in the set of probability distribution functions and their applications in queueing theory

Tomasz Rolski

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CONTENTSIntroduction......................................................................................................................................... 51. n-Monotonic functions on (— ∞, ∞)........................................................................................... 62. Order relations in the set of probability distribution functions....................................................... 12 2.1. Preliminary concepts...............................................................................................................

L p -improving properties of measures of positive energy dimension

Kathryn E. Hare, Maria Roginskaya (2005)

Colloquium Mathematicae

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A measure is called L p -improving if it acts by convolution as a bounded operator from L p to L q for some q > p. Positive measures which are L p -improving are known to have positive Hausdorff dimension. We extend this result to complex L p -improving measures and show that even their energy dimension is positive. Measures of positive energy dimension are seen to be the Lipschitz measures and are characterized in terms of their improving behaviour on a subset of L p -functions.

Probability distribution solutions of a general linear equation of infinite order, II

Tomasz Kochanek, Janusz Morawiec (2010)

Annales Polonici Mathematici

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Let (Ω,,P) be a probability space and let τ: ℝ × Ω → ℝ be a mapping strictly increasing and continuous with respect to the first variable, and -measurable with respect to the second variable. We discuss the problem of existence of probability distribution solutions of the general linear equation F ( x ) = Ω F ( τ ( x , ω ) ) P ( d ω ) . We extend our uniqueness-type theorems obtained in Ann. Polon. Math. 95 (2009), 103-114.

Denseness and Borel complexity of some sets of vector measures

Zbigniew Lipecki (2004)

Studia Mathematica

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Let ν be a positive measure on a σ-algebra Σ of subsets of some set and let X be a Banach space. Denote by ca(Σ,X) the Banach space of X-valued measures on Σ, equipped with the uniform norm, and by ca(Σ,ν,X) its closed subspace consisting of those measures which vanish at every ν-null set. We are concerned with the subsets ν ( X ) and ν ( X ) of ca(Σ,X) defined by the conditions |φ| = ν and |φ| ≥ ν, respectively, where |φ| stands for the variation of φ ∈ ca(Σ,X). We establish necessary and sufficient...

Self-affine measures that are L p -improving

Kathryn E. Hare (2015)

Colloquium Mathematicae

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A measure is called L p -improving if it acts by convolution as a bounded operator from L q to L² for some q < 2. Interesting examples include Riesz product measures, Cantor measures and certain measures on curves. We show that equicontractive, self-similar measures are L p -improving if and only if they satisfy a suitable linear independence property. Certain self-affine measures are also seen to be L p -improving.

Simplices rarely contain their circumcenter in high dimensions

Jon Eivind Vatne (2017)

Applications of Mathematics

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Acute triangles are defined by having all angles less than π / 2 , and are characterized as the triangles containing their circumcenter in the interior. For simplices of dimension n 3 , acuteness is defined by demanding that all dihedral angles between ( n - 1 ) -dimensional faces are smaller than π / 2 . However, there are, in a practical sense, too few acute simplices in general. This is unfortunate, since the acuteness property provides good qualitative features for finite element methods. The property...

Path functionals over Wasserstein spaces

Alessio Brancolini, Giuseppe Buttazzo, Filippo Santambrogio (2006)

Journal of the European Mathematical Society

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Given a metric space X we consider a general class of functionals which measure the cost of a path in X joining two given points x 0 and x 1 , providing abstract existence results for optimal paths. The results are then applied to the case when X is aWasserstein space of probabilities on a given set Ω and the cost of a path depends on the value of classical functionals over measures. Conditions for linking arbitrary extremal measures μ 0 and μ 1 by means of finite cost paths are given. ...