## Matchings of exponential tail on coin flips in Z^d

- Date: 03/28/2007

Lecturer(s):

Adam Timar (University of British Columbia)

Location:

University of British Columbia

Topic:

We construct a translation-invariant matching between vertices of

different labels of Bernoulli(1/2) percolation on Z^d, in such a way

that the probability that a vertex is at distance > r from its pair

decays as an exponential function of the d-2'nd power of r. Our method

implies earlier results about matching n uniformly distributed red

points with n uniformly distributed blue points in the unit square with

minimal average distance. Other consequences to invariant matchings in

R^d and optimal matchings in the unit cube are also presented.

Other Information:

Probability Seminar 2007