5 problems

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Hatami–Lovász–Szegedy conjecture on FIID approximations of optimization problems
Let $\mathbb{T}_d$ be the infinite $d$ -regular tree, and consider processes on it that are factors of independent identically distributed labels. A random $d$ -regular graph is a gr…
Conjecturerefutedfactor-of-iid percolation random-regular-graphsarXiv posted 2 days ago
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Szegedy's sparse tail-triviality conjecture for FIID measures
A probability measure $(\Omega^V,\mathbb{P})$ on configurations over an infinite graph is a factor of IID (FIID) measure if it is obtained as a factor of an IID process. A function…
Conjectureopenfactor-of-iid spin-systems tail-trivialityarXiv posted 2 days ago
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Silly conjecture on factor-of-iid chromatic number of regular trees
Let $T_r$ be the infinite $r$ -regular tree, and let $\chi_{fiid}(T_r)$ denote its factor-of-iid chromatic number, the least number of colors in a proper coloring of $T_r$ produced…
Conjectureopenfactor-of-iid graph-coloring regular-treesarXiv posted 2 days ago
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Equivalence of factor-of-iid structures on amenable transitive graphs
Equivalence conjecture. For amenable graphs $G$ , these four assertions are equivalent.
Conjectureopenamenable-graphs factor-of-iid graph-colouringsarXiv posted 2 days ago
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Szegedy's conjecture on independent sets in random regular graphs
Szegedy's conjecture. This limit is equal to $i(\mathcal{T}_d)$ .
Conjectureopenfactor-of-iid independent-sets random-regular-graphsarXiv posted 2 days ago

5 problems

Hatami–Lovász–Szegedy conjecture on FIID approximations of optimization problems

Szegedy's sparse tail-triviality conjecture for FIID measures

Silly conjecture on factor-of-iid chromatic number of regular trees

Equivalence of factor-of-iid structures on amenable transitive graphs

Szegedy's conjecture on independent sets in random regular graphs