HP Labs Technical Reports
Click here for full text:
A Law of Large Numbers for Random Hierarchical Sequences
Hambly, B.M.; O'Connell, Neil
HPLBRIMS200013
Keyword(s): renormalization; Banach lattice; homogenization on fractals
Abstract: We generate a hierarchical sequence of random variables from a map taking k copies of a Banach space to itself. With a simple assumption on the map and an integrability condition for the initial random variables we prove that the renormalized sequence converges almost surely to a constant. We apply this result to the homogenization of Laplace operators on fractals. Notes: B.M. Hambly, Department of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW UK
16 Pages
Back to Index
