About Thinning Invariant Partition Structures |
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Authors: | Shannon Starr Brigitta Vermesi Ang Wei |
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Affiliation: | 1. Department of Mathematics, University of Rochester, Rochester, NY, 14627, USA 2. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA
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Abstract: | Bernoulli-p thinning has been well-studied for point processes. Here we consider three other cases: (1) sequences (X 1,X 2,??); (2) gaps of such sequences (X n+1?X 1) n???; (3) partition structures. For the first case we characterize the distributions which are simultaneously invariant under Bernoulli-p thinning for all p??(0,1]. Based on this, we make conjectures for the latter two cases, and provide a potential approach for proof. We explain the relation to spin glasses, which is complementary to important previous work of Aizenman and Ruzmaikina, Arguin, and Shkolnikov. |
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