6 problems

Let $U_{\phi}$ be the set appearing in the source, and let $\mu$ be a non-trivial gradient Gibbs measure, meaning that $\mu$-almost surely $Z_{\Lambda}(\phi)<\infty$ for every fini…

Consider perturbed simply attractive potentials, including anisotropic potentials, meaning potentials that are not necessarily isotropic. Let the variational principle be the relat…

Consider a sequence of finite regions converging to a fixed shape, and let $(s,t)$ be the tilt given by the variational principle wherever that tilt is defined. Let $\mu_{s,t}$ be…

Uniform bounds conjecture. There exist constants $0<c<C$, depending on all the data, such that $$

Let $(X,d)$ be a compact metric space, let $f:X\to X$ be a homeomorphism, and let $\mathcal{M}(f,X)$ be the invariant Borel probability measures for $f$. For $r>0$, define the $r$-…

The variational principle for skew Young tableaux. The function $g(t,x)$ maximizes