9 problems

Let $G$ be a transitive graph with non-negative Ollivier--Ricci curvature. Recall that two metric spaces are quasi-isometric if they are equivalent up to multiplicative and additiv…

Let $G$ be an infinite, connected, transitive, simple graph of vertex degree $d$ that is not one-dimensional, and let $p_c(G)$ be its Bernoulli bond percolation critical probabilit…

Let $\mathcal G_d^*$ be the class of infinite transitive graphs of degree $d$ that are not one-dimensional. For a graph $G$ with origin $o$, let $S_r$ be the sphere of radius $r$ a…

Let $\mathcal G_d^*$ be the class of infinite transitive graphs of degree $d$ that are not one-dimensional. For a graph $G$ with origin $o$, let $S_r$ be the sphere of radius $r$ a…

Let $G=(V,E)$ be a locally finite, connected, transitive, transient graph with spectral radius $\rho$, fix $o\in V$, and let $(X_n)_{n\geq 0}$ be simple random walk started at $o$.…

The first-return asymptotic conjecture. One has $f_n\asymp u_n$, and more precisely

Schramm's locality conjecture. Then

Let $\Gamma$ be a two-ended transitive graph. A finite Hamilton cover is a finite collection of Hamiltonian spanning subgraphs whose union covers the relevant graph structure, as i…

Random-eigenvector probability conjecture. For any transitive graph $G$,