Monotone expansion
Jean Bourgain, Amir Yehudayoff · 2012
This work presents an explicit construction of a family of monotone expanders, which are bi-partite expander graphs whose edge-set is defined by (partial) monotone functions. The family is essentially defined by the Mobius action of SL2(R), the group of 2 x 2 matrices with determinant one, on the interval [0,1]. No other proof-of-existence for monotone expanders is known, not even using the probabilistic method.