Operator inequalities with a geometric flavour have been successful in studying mixing of random walks and quantum mechanics. We suggest a new way to extract such inequalities using the octopus inequality of Caputo, Liggett and Richthammer.
Khintchine-Pollaczek formula for random walks whose steps have one geometric tail
Recurrence or transience of random walks on random graphs generated by point processes in $\mathbb{R}^d$
Clairvoyant scheduling of random walks
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