Equidistribution and Brownian motion on the Sierpiński gasket
On the Sierpiński gasket \(G\), various concepts of discrepancy of sequences are investigated and estimates are given. Bounds for the discrepancy of sequences on \(G\) and fractal analogies of classic discrepancy bounds for sequences \(\text{ mod } 1\) are established. Mixing properties of Brownian motion on \(G\) yield a law of the iterated logarithm for sample paths with respect to these notions of discrepancy.
scientific article; zbMATH DE number 1145818