15 problems

Schramm's locality conjecture for the percolation critical probability
arXiv@arxiv
Let $(G,o)$ and $(H,o')$ be rooted graphs, with the space of isomorphism classes of rooted graphs equipped with the local metric. Restrict to transitive graphs satisfying…
Conjecturesolvedlocal-convergence percolation random-graphs
0
Locality of the critical percolation probability
arXiv@arxiv
For a sequence of graphs whose local limits determine their local structure, consider the critical percolation probability $p_c$ for transitive graphs, where $p_c$ is the infimum o…
Conjecturesolvedlocal-convergence percolation random-graphs
1
Universal local-limit conjecture for mandatory and blocking edges
arXiv@arxiv
Universal mandatory and blocking edge conjecture. The marked random graphs
Conjectureopenlocal-convergence matchings random-graphs
0
The local weak limit conjecture for random intersection graphs
arXiv@arxiv
Construct the locally finite connected rooted random graph $G^\bullet$ from the partially labeled rooted random tree $T^\bullet$ as described in the source: even-generation vertice…
Conjectureopenlocal-convergence probability random-intersection-graphs
0
Infinite-condensation-root convergence conjecture for expansive Galton–Watson trees
arXiv@arxiv
Infinite-condensation-root conjecture. If $\frak{b}=+$ and $f(R_c)=+$ , then $\tau_n$ converges locally in distribution towards a limit $\tau^$ whose root has an infinite number of…
Conjectureopenbranching-processes galton-watson-processes local-convergence
1
Continuity at infinity conjecture for limiting Galton–Watson trees
arXiv@arxiv
Continuity-at-infinity conjecture. If $R_c>1$ , then $\tau^\theta$ converges locally in distribution towards $\tau^$ as $\theta\to+$ .
Conjectureopenbranching-processes galton-watson-processes local-convergence
1
High-regime local convergence conjecture for expansive Galton–Watson trees
arXiv@arxiv
High-regime convergence conjecture. If $R_c>1$ , equivalently if $W$ has some positive exponential moments, then $\tau_n$ converges locally in distribution towards $\tau^$ in the hi…
Conjectureopenbranching-processes galton-watson-processes local-convergence
1
Compactified local convergence for unrooted minor-excluding graphs
arXiv@arxiv
Compactified unrooted convergence conjecture. The sequence $G_n$ converges weakly with respect to $d$ .
Conjectureopengraph-minors local-convergence random-graphs
0
Compactified weak convergence for rooted minor-excluding graphs
arXiv@arxiv
Compactified rooted convergence conjecture. The sequence $R_n$ converges weakly with respect to $d$ .
Conjectureopengraph-minors local-convergence random-graphs
0
Weak convergence for rooted graphs excluding a finite set of minors
arXiv@arxiv
Rooted minor-exclusion convergence conjecture. The sequence $R_n$ converges weakly.
Conjectureopengraph-minors local-convergence random-graphs
0
Local convergence for uniformly random graphs from minor-closed families
arXiv@arxiv
Minor-closed-family convergence conjecture. The uniformly random $n$ -vertex graph from any minor-closed family converges in this sense.
Conjectureopengraph-minors local-convergence random-graphs
0
Local convergence under conditioning of large total mass
arXiv@arxiv
Let $X$ be the canonical process under the excursion measure $\mathbf{N}$ of the strong Markov process $X-I$ at zero. Write $H$ for the height process, $\zeta$ for its lifetime, an…
Problemopenbranching-processes levy-trees local-convergence
0
Local convergence under conditioning of large maximal degree
arXiv@arxiv
Let $X$ be the canonical process under the excursion measure $\mathbf{N}$ of the strong Markov process $X-I$ at zero. Write $H$ for the height process, $\zeta$ for its lifetime, an…
Conjectureopenbranching-processes levy-trees local-convergence
0
Aldous–Lyons conjecture for graphings
arXiv@arxiv
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…
Conjectureopengraphings local-convergence unimodularity
0
Local convergence conjecture for Schaeffer trees in large quadrangulations
arXiv@arxiv
Local convergence conjecture. The pair
Conjectureopenlocal-convergence random-quadrangulations random-trees
0