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math.PR2022
Logarithmic corrections to the Alexander-Orbach conjecture for the four-dimensional uniform spanning tree
Noah Halberstam, Tom Hutchcroft
We compute the precise logarithmic corrections to Alexander-Orbach behaviour for various quantities describing the geometric and spectral properties of the four-dimensional uniform…
math.PR2022
Most transient random walks have infinitely many cut times
Noah Halberstam, Tom Hutchcroft
We prove that if is a random walk on a transient graph such that the Green's function decays at least polynomially along the random walk, then h…