5 problems

Let $T$ be the number of iterations and let $a,b\to 1,\ldots,n$ index replicas. For $1\leq s\leq t\leq T$, define the order parameters $Q_{u,ab}^{st}$ and $Q_{v,ab}^{st}$ as the pa…

The replica integral is represented, for integer $n$, as a sum over saddle-point sectors indexed by $l=0,\ldots,2n$, with the central sector $l=n$ giving the dominant non-oscillati…

Consider the generalized linear model with orthogonally invariant design, and let $\widehat{\beta}_{\mathrm{B}}=\mathbb{E}[\beta_*\mid X,y]$ be the posterior mean estimator. Let…

Scalar-overlap restriction conjecture. This restriction of the replica formula for the free energy is correct in general, including outside the setting of abelian groups.

Bosonic replica reliability conjecture. The statement that bosonic replicas are as good and reliable as fermionic replicas should hold in full generality, regardless of which parti…