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Extremal and optimal solutions in the transshipment problem

Viktor Beneš (1992)

Commentationes Mathematicae Universitatis Carolinae

The paper yields an investigation of the set of all finite measures on the product space with given difference of marginals. Extremal points of this set are characterized and constructed. Sets of uniqueness are studied in the relation to marginal problem. In the optimization problem the support of the optimal measure is described for a class of cost functions. In an example the optimal value is reached by an unbounded sequence of measures.

Extremal points of high-dimensional random walks and mixing times of a brownian motion on the sphere

Ronen Eldan (2014)

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

We derive asymptotics for the probability that the origin is an extremal point of a random walk in ℝ n . We show that in order for the probability to be roughly 1 / 2 , the number of steps of the random walk should be between e n / ( C log n ) and e C n log n for some constant C g t ; 0 . As a result, we attain a bound for the π 2 -covering time of a spherical Brownian motion.

Extremal sections of complex l p -balls, 0 < p ≤ 2

Alexander Koldobsky, Marisa Zymonopoulou (2003)

Studia Mathematica

We study the extremal volume of central hyperplane sections of complex n-dimensional l p -balls with 0 < p ≤ 2. We show that the minimum corresponds to hyperplanes orthogonal to vectors ξ = (ξ¹,...,ξⁿ) ∈ ℂⁿ with |ξ¹| = ... = |ξⁿ|, and the maximum corresponds to hyperplanes orthogonal to vectors with only one non-zero coordinate.

Extremal solutions of a general marginal problem

Petra Linhartová (1991)

Commentationes Mathematicae Universitatis Carolinae

The characterization of extremal points of the set of probability measures with given marginals is given in the general context of a marginal system. The sets of marginal uniqueness are studied and an example is added to illustrate the theory.

Extreme and exposed representing measures of the disk algebra

Alex Heinis, Jan Wiegerinck (2000)

Annales Polonici Mathematici

We study the extreme and exposed points of the convex set consisting of representing measures of the disk algebra, supported in the closed unit disk. A boundary point of this set is shown to be extreme (and even exposed) if its support inside the open unit disk consists of two points that do not lie on the same radius of the disk. If its support inside the unit disk consists of 3 or more points, it is very seldom an extreme point. We also give a necessary condition for extreme points to be exposed...

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