Graduate Program in Mathematics.Altok, Serdar.Charyyev, Polat.2023-03-162023-03-162012.MATH 2012 C43https://digitalarchive.library.bogazici.edu.tr/handle/123456789/15263Let LSFC n denote the length of the path connecting n random points uniformly distributed over the unit square obtained by the space lling curve heuristic. For a Hilbert type of space lling curve such as; Peano, Moore, Sierpinski and Polya, we prove that for some number K, we have, for all ... ; where K depends only on the space ling curve. This thesis is motivated by the work of Gao and Steele [1], where they found an almost Gaussian tail bound for a broad class of space lling curves. By adapting the method of Rhee and Talagrand [2], we have obtained an exact Gaussian tail bound for the length of the path obtained by the space lling curve..30 cm.Gaussian processes.Spectral theory (Mathematics)ix, 63 leaves ;