The five-dimensional Watson integral
Find a closed form for the five-dimensional Watson integral W5 ≈ 0.2312616250, which fixes the return probability of a random walk on Z^5.
Problems
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Matching problems
The site percolation threshold of the square lattice
Find a closed form for the site percolation threshold of the square lattice, p_c ≈ 0.5927460508; bond percolation has p_c = 1/2.
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Prove that the deficit of maximal flow through oriented bond percolation behaves like sqrt(2(1 − p)) as p tends to 1.
Openper David Aldous's open problems, 2026-10-20
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Find a closed form for the entropy per site of monomer-dimer configurations on the square lattice, h ≈ 0.6627989727.
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Find a closed form for the hard-square entropy constant κ ≈ 1.5030480825, the growth rate of independent sets in the square grid.
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Prove that two competing growth processes on the lattice cannot both grow forever when their speeds differ.
Openper AIM Problem Lists, 2026-10-20
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