5 problems

A random overlap structure (ROSt) is a random structure encoding overlaps between states. A $p$-th power cavity field is the cavity field obtained from the $p$-th power interaction…

A random overlap structure (ROSt) is a random structure encoding overlaps between states; its law is stochastically stable when it is invariant under the relevant stochastic-stabil…

Let the Ghirlanda–Guerra identities be imposed on the laws of random overlap structures, and consider the convex set of laws of stochastically stable ROSts. Ghirlanda–Guerra extrem…

Let $\ROSt$ be a random overlap structure with law $\mathbb{P}$, and let $\mu$ be its sampling measure. Suppose that $\ROSt$ is stochastically stable for the cavity fields $l_p$ fo…

Let $(\xi,Q)$ be a Ruelle probability cascade (RPC), constructed from a Poisson–Dirichlet variable and a Bolthausen–Sznitman coalescent. More generally, consider random overlap str…