𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Coupling Surfaces and Weak Bernoulli in One and Higher Dimensions

✍ Scribed by Robert M. Burton; Jeffrey E. Steif

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
303 KB
Volume
132
Category
Article
ISSN
0001-8708

No coin nor oath required. For personal study only.

✦ Synopsis

We propose a notion of weak Bernoulli in all dimensions which generalizes the usual definition in dimension 1. The key idea is the concept of a coupling surface. We relate this notion to previously studied properties and discuss a number of possible variants in dimension 1. We also show that the Ising model, at low temperature, is weak Bernoulli with an explicit description of the coupling surface.

πŸ“œ SIMILAR VOLUMES

On Wavelets and Prewavelets with Vanishi
On Wavelets and Prewavelets with Vanishing Moments in Higher Dimensions
πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 443 KB

Using an approximation theory approach, we prove that a scaling function with suitable polynomial decay satisfies the Strang-Fix condition of order r # N if and only if the elements of any prewavelet set [ & ] & # E\* with polynomial decay of the same order have vanishing integral moments up to orde

Estimation of densities of probability a
Estimation of densities of probability and regression surfaces in one or two dimensions
✍ Christian Duhamel; GΓ©rard Parlant πŸ“‚ Article πŸ“… 1984 πŸ› Elsevier Science 🌐 English βš– 513 KB

The FORTRAN programs presented make it possible to build curves and surfaces of densities for the Lebesgue-measure, when one has a sample ofn independent observations of a random variable in one or two dimensions and when this number n can be high (many thousands). The method uses kernel-estimators