HP Labs Technical Reports
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Renormalization of Hierarchical Sequences
Hambly, Ben; O'Connell, Neil
HPLBRIMS200003
Keyword(s): renormalization; hierarchical sequences; electrical networks; conductance; vectorvalued martingales; Banach lattices; homogenization; 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. This result can be applied to the renormalization of electrical networks and homogenization of Laplace operators on fractals. Notes: Ben Hambly, Department of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, UK
19 Pages
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