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A ``Thinning'' Analogue of de Finetti's Theorem
Probability| Speaker: | Shannon Starr, University of Rochester |
| Location: | 2112 MSB |
| Start time: | Tue, Jan 9 2007, 2:10PM |
I will present a simple generalization of de Finetti's theorem, wherein exchangeability -- i.e. permutation invariance -- is replaced by ``thinning-invariance''. ``Thinning'' is a random dynamics acting on n-tuples by deleting one component, at random, and left-justifying the remaining n-1 components, keeping their relative order fixed. This has applications to mean-field theory in 1-d spin systems when both the range of the interaction and the size of the lattice approach infinity together, but where the interaction may be asymmetric. Graduate students are welcome: no prior knowledge of de Finetti's theorem will be assumed.