7 problems

Let $(X,bcmu)$ be a standard probability space, and let $\mathcal{G}$ be a locally finite Borel graph on $X$. Say that $\mathcal{G}$ is $\mu$-nowhere smooth if no positive-measure…

Compilation-equivalence characterization conjecture. If

Let $f(k)$ be the smallest integer $f$ such that for every $d\in[k]$ the following holds. Let $G$ be an arbitrary finite graph such that every degree is at most $d$, except at most…

A graphing is a probability-preserving graph structure representing a bounded-degree graph limit; a graphing is typical if it arises almost surely as the local-global limit of an i…

Let a modeling be a measurable graph equipped with a probability measure for which first-order definable sets are measurable. A graph has bounded degree if its vertex degrees are u…

A graphing is a bounded-degree Borel graph satisfying the Intrinsic Mass Transport Principle. A bounded-degree graph sequence has a Benjamini–Schramm limit when the distribution of…

Bernoulli-sequence conjecture. With probability one, $(G_n)_{n=1}^\infty$ is a Bernoulli sequence. Equivalently, its limit object is the Bernoulli graphing produced from the $d$-re…