2 problems

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Favourite-site upper-function integral-test conjecture
Let $V(n)$ denote a favourite site of simple random walk at time $n$ , and let $\nu>1$ be the constant from the Brownian favourite-site upper-tail conjecture. For any non-decreasing…
Conjecturerefutedintegral-tests local-times random-walkarXiv posted 2 days ago
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An integral test for the stationary pinned string
Integral-test conjecture.
Conjectureopenintegral-tests random-strings stationary-pinned-stringarXiv posted 2 days ago

Favourite-site upper-function integral-test conjecture