Abstract: | Given a convex body K ⊂ R d, what is the probability that a randomly chosen congruent copy, K*, of K is lattice‐point free, that is, K*∩ Z d = ∅︁? Here Z d is the usual lattice of integer points in R d. Luckily, the underlying probability is well defined since integer translations of K can be factored out. The question came up in connection with integer programming. We explain what the answer is for convex bodies of large enough volume. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007 |