Natural languages and random structures are given for which there are sentences A with no limit probability, yet for every A the difference between the probabilities that A holds on random structures of sizes n and n + 1 approaches zero with n.
First order zero–one laws for random graphs on the circle
✍ Scribed by Gregory L. McColm
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 329 KB
- Volume
- 14
- Category
- Article
- ISSN
- 1042-9832
No coin nor oath required. For personal study only.
✦ Synopsis
We look at a competitor of the Erdos᎐Renyi models of random graphs, one ˝ẃ Ž .x proposed in E. Gilbert J. Soc. Indust. Appl. Math. 9:4, 533᎐543 1961 : given ␦ ) 0 and a metric space X of diameter ) ␦ , scatter n vertices at random on X and connect those of distance -␦ apart: we get a random graph G X . Letting X be a circle, we look at zero-one
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