2 problems

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Erdős–Révész conjecture on favorite sites of the simple random walk
Let a simple random walk on $\mathbb{Z}$ have local times, and call the sites attaining the maximal local time its favorite sites. The set of favorite sites is tight if it remains…
Conjectureopenfavorite-sites local-times random-walksarXiv posted 2 days ago
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Tóth's conjecture on finitely many three-favorite-site occurrences
Tóth's conjecture. The number of times at which the walk is at one of exactly three favorite sites is finite almost surely:
Conjectureopenfavorite-sites local-times random-walksarXiv posted 2 days ago

Erdős–Révész conjecture on favorite sites of the simple random walk