Equipartition of sphere measures by hyperplanes

Equipartition of Two Measures by a 4-Fan

We show that, given two probability measures in the plane, there exists a 4-fan that simultaneously equipartitions them. In other words, there is a point and four half-lines emanating from it such that each of the four sectors have measure 1 4 in both measures.

Reconstruction sequences and equipartition measures: An examination of the asymptotic equipartition property

We consider a stationary source emitting letters from a finite al­ phabet A. The source is described by a stationary probability measure a on the space 0 := AlN of sequences of letters. Denote by On the set of words of length n and by an the probability measure induced on On by a. \Ve consider sequences {rneOn : n E IN} having special properties. Call {rneOn: n E IN} a sup­ porting sequence for...

Isoperimetry and stability of hyperplanes for product probability measures

An asymptotic equipartition property for measures on model spaces

Let G be a sofic group, and let Σ “ pσnqně1 be a sofic approximation to it. For a probability-preserving G-system, a variant of the sofic entropy relative to Σ has recently been defined in terms of sequences of measures on its model spaces that ‘converge’ to the system in a certain sense. Here we prove that, in order to study this notion, one may restrict attention to those sequences that have ...

Computing hypercircles by moving hyperplanes

Let K be a field of characteristic zero, α algebraic of degree n over K. Given a proper parametrization ψ of a rational curve C, we present a new algorithm to compute the hypercircle associated to the parametrization ψ. As a consequence, we can decide if C is defined over K and, if not, to compute the minimum field of definition of C containing K. The algorithm exploits the conjugate curves of ...