Physics Commons^™

Globe-Hopping, Dmitry Chistikov, Olga Goulko, Adrian Kent, Mike Paterson

Physics Faculty Publications and Presentations

We consider versions of the grasshopper problem [1] on the circle and the sphere, which are relevant to Bell inequalities. For a circle of circumference 2π, we show that for unconstrained lawns of any length and arbitrary jump lengths, the supremum of the probability for the grasshopper’s jump to stay on the lawn is one. For antipodal lawns, which by definition contain precisely one of each pair of opposite points and have length π, we show this is true except when the jump length φ is of the form π p/q with p, q coprime …