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Title: Pattern Theorem for the Hexagonal Lattice
Keywords: Cubic Lattice, Hexagonal Lattice, Self-avoiding Random Walk, Linear Polymer, Patterns, Connective Constant
Issue Date: 29-Jan-2009
Citation: PRITHA GUHA (2009-01-29). Pattern Theorem for the Hexagonal Lattice. ScholarBank@NUS Repository.
Abstract: A linear polymer can be thought of as a flexible long chain of beads that follows a lattice where each bead represents a monomer unit. It can be modelled as a self-avoiding random walk on a lattice. When the linear polymer is in a chemical solution and is following a 2-dimensional hexagonal lattice, it becomes self-entangled. It can be shown that in all su ciently long polymers a pattern is present. Kesten's Pattern Theorem, which was originally proved for self-avoiding walks on cubic lattices, is extended to the self-avoiding walks on hexagonal lattices. Properties of the hexagonal lattice, self-avoiding walks on the hexagonal lattice and the connective constant for the hexagonal lattice are then provided. Further, computation of the probability of a self-avoiding walk on the hexagonal lattice encircling the points (1/2,1/2) and (1/2,-1/2) is discussed.
Appears in Collections:Master's Theses (Open)

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