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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 $\frac{π}{2}$ -covering time of a spherical Brownian motion.

Generalized Breadths, Circular Cantor Sets, and the Least Area UCC .

Gy. Elekes (1994)

Discrete & computational geometry

Hyperplane conjecture for quotient spaces of Lp.

Marius Junge (1994)

Forum mathematicum

Illumination bodies and affine surface area

Elisabeth Werner (1994)

Studia Mathematica

We show that the affine surface area as(∂K) of a convex body K in $ℝ^{n}$ can be computed as $a s (\partial K) = l i m_{δ \to 0} d_{n} (v o l_{n} (K^{δ}) - v o l_{n} (K)) / (δ^{2 / (n + 1)})$ where $d_{n}$ is a constant and $K^{δ}$ is the illumination body.

Inequalities Between Successive Minima and Intrinsic Volumes of a Convey Body.

Martin Henk (1990)

Monatshefte für Mathematik

Isoperimetric inequalities for quermassintegrals

Neil S. Trudinger (1994)

Annales de l'I.H.P. Analyse non linéaire

Lattice Inequalities for Convex Bodies and Arbitrary Lattices.

Uwe Schnell (1993)

Monatshefte für Mathematik

Mahler's Conjecture and Wavelets.

K. Ball (1995)

Discrete & computational geometry

Maximum convex hulls of connected systems of segments and of polyominoes.

Bezdek, Károly, Braß, Peter, Harborth, Heiko (1994)

Beiträge zur Algebra und Geometrie

Minimum-area axially symmetric convex bodies containing a triangle and its measure of axial symmetry.

Lassak, Marek, Nowicka, Monika (2009)

Beiträge zur Algebra und Geometrie

O Pickově vzorci a rozměňování peněz

Marie Holíková (2016)

Pokroky matematiky, fyziky a astronomie

V tomto článku představíme jeden méně známý elegantní důkaz Pickova vzorce pro výpočet obsahu jednoduchých mřížových mnohoúhelníků, který je založen na tzv. úhlech viditelnosti. Princip tohoto důkazu lze částečně použít i k odvození zobecněného Pickova vzorce pro mřížové mnohoúhelníky, které nejsou jednoduché. Dále naznačíme potíže spojené s prostorovou analogií Pickova vzorce. Nakonec ukážeme, jak Pickův vzorec souvisí s rozměňováním peněz.

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Computing the Volume, Counting Integral Points, and Exponential Sums.

Confirmation of Matheron's conjecture on the covariogram of a planar convex body

Die Dehnsche Zerlegungsinvariante für hyperbolische Polyederbausteine.

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

Generalized Breadths, Circular Cantor Sets, and the Least Area UCC .

Hyperplane conjecture for quotient spaces of Lp.

Illumination bodies and affine surface area

Inequalities Between Successive Minima and Intrinsic Volumes of a Convey Body.

Isoperimetric inequalities for quermassintegrals

Lattice Inequalities for Convex Bodies and Arbitrary Lattices.

Mahler's Conjecture and Wavelets.

Maximum convex hulls of connected systems of segments and of polyominoes.

Minimum-area axially symmetric convex bodies containing a triangle and its measure of axial symmetry.

O Pickově vzorci a rozměňování peněz

On a discrete Dido-type question.

On boundary arcs joining antipodal points of a planar convex body.

On H. Weyl and H. Minkowski polynomials.

On Intersystolic Inequalities in Dimension 3.

On rhombic dodecahedra.

On Schläfli's reduction formula.

Currently displaying 21 – 40 of 77