11 problems

Let ${P}^0$ be the annealed law of an i.i.d. random walk in random environment on $\mathbb Z^d$, and let $S^{d-1}$ be the set of unit vectors in $\mathbb R^d$. For…

For $p\in(0,1)$, let $G(n,p)$ be the binomial random graph on $[n]:=\{1,\ldots,n\}$, with each possible edge present independently with probability $p$. An EMSO(FO$^2$) sentence is…

Let $\alpha\in(0,1)$ be irrational, let $p_n=n^{-\alpha}$, and let $G(n,p_n)$ be the random graph on $[n]=\{1,\dotsc,n\}$ in which edges are drawn independently with probability…

The finitary zero-one law is used to obtain bounds on metastable statements in probability theory. The authors give examples involving Kolmogorov's three-series theorem and bond pe…

Let $\underline{X}$ be the random process and let $\pi$ be a finitary permutation as in Theorem 1.1, whose conclusion concerns the equality of the distributions of $\underline{X}$…

Let $X$ be the Lévy process in the paper, let $\tau_1$ be its first killing time in the resurrection construction, let $\tau_n$ be the successive killing times, let $\tau$ denote t…

Let $\mathcal{L}$ be a finite relational language with relational arity parameter $r_{\mathcal{L}}\geq 2$, and let $\mathcal{H}$ be a fast-growing hereditary $\mathcal{L}$-property…

Let $r\geq 2$ be an integer, and let $M_r$ be the class of finite metric spaces whose nonzero distances belong to a prescribed set of $r$ distances, with language $\mathcal{L}_r$.…

Let $J$ be the interval of $L$-functions described in the surrounding classification, consisting entirely of convergence laws. Maximality conjecture. We conjecture that $J$ is a ma…

Let $r\geq 3$ be an odd integer, and let $M_r(n)$ denote the class of finite metric spaces on $[n]$ with distances in the relevant $r$-element distance set. Let $\mathcal{L}_r$ be…

Zero-one conjecture for permutable events. Any permutable event in Protocol1 is either fully plausible or unsupported.