About Thinning Invariant Partition Structures

摘要

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.