Loop-erased self-avoiding random walk in two and three dimensions |
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| Authors: | Gregory F Lawler |
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| Institution: | (1) Courant Institute of Mathematical Sciences, New York University, 10012 New York, New York;(2) Present address: Department of Mathematics, Duke University, 27706 Durham, North Carolina |
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| Abstract: | If (n) is the position of the self-avoiding random walk in 
d
obtained by erasing loops from simple random walk, then it is proved that the mean square displacementE(¦(n)¦2) grows at least as fast as the Flory predictions for the usual SAW, i.e., at least as fast asn
3/2 ford=2 andn
6/5 ford=3. In particular, if the mean square displacement of the usual SAW grows liken
1.18... ind=3, as expected, then the loop-erased process is in a different universality class. |
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| Keywords: | Self-avoiding random walk loop-erased walk Laplacian random walk polymer models Flory exponents |
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