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Properties of ergodic random mosaic processes

✍ Scribed by Richard Cowan

Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
677 KB
Volume
97
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The consequences of an ergodic assumption for mosaic processes of random convex polygons are explored in detail. Under certain regularity conditions on the β€œsmallness” and β€œlargeness” of polygons it is shown that the geometric characteristics of the so‐called β€œtypical” polygons do in fact exist. New formulae concerning these characteristics are given. The polygon process formed by a Poisson line process is considered as an example of the general theory and, as a result, certain properties of this example which were previously given heuristically, are proved. Edge effects are treated rigorously.

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✍ Z. PluhaΕ™; H.A. WeidenmΓΌller πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 191 KB

Using Efetov's supersymmetry method, we prove the ergodicity of a wide class of unitary random-matrix ensembles. We do so by showing that the connected part of the autocorrelation function of any observable vanishes asymptotically. The essential elements of the proof consist in a polar decomposition