Wei-Tao Huang

Exact Endpoint Asymptotics and Almost-Sure Limits for Uniform Empirical Measures in Two Dimensions

For the empirical measure of the first $n$ points of one infinite sequence of independent uniform samples in the unit square, we identify the leading constant in the bounded-Lipschitz distance to area measure, equivalently in $W_1$, both in expectation and almost surely along all sample sizes. The constant is $c_*=\kap...