We obtain bounds to show that the pressure of a two-body, mean-field spin
glass is a Lipschitz function of the underlying distribution of the random
coupling constants, with respect to a particular semi-norm. This allows us to
re-derive a result of Carmona and Hu, on the universality of the SK model, by a
different proof, and to generalize this result to the Viana-Bray model. We also
prove another bound, suitable when the coupling constants are not independent,
which is what is necessary if one wants to consider ``canonical'' instead of
``grand canonical'' versions of the SK and Viana-Bray models. Finally, we
review Viana-Bray type models, using the language of L\'evy processes, which is
natural in this context.Comment: 15 pages, minor revision
Bernoulli-p thinning has been well-studied for point processes. Here we consider three other cases: (1) sequences (X1, X2, . . . ); (2) gaps of such sequences (Xn+1 − X1) n∈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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