A Lower Bound on the Growth Exponent for Loop-Erased Random Walk in Two Dimensions

Gregory F. Lawler

ESAIM: Probability and Statistics (2010)

  • Volume: 3, page 1-21
  • ISSN: 1292-8100

Abstract

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The growth exponent α for loop-erased or Laplacian random walk on the integer lattice is defined by saying that the expected time to reach the sphere of radius n is of order nα. We prove that in two dimensions, the growth exponent is strictly greater than one. The proof uses a known estimate on the third moment of the escape probability and an improvement on the discrete Beurling projection theorem.

How to cite

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Lawler, Gregory F.. "A Lower Bound on the Growth Exponent for Loop-Erased Random Walk in Two Dimensions." ESAIM: Probability and Statistics 3 (2010): 1-21. <http://eudml.org/doc/197727>.

@article{Lawler2010,
abstract = { The growth exponent α for loop-erased or Laplacian random walk on the integer lattice is defined by saying that the expected time to reach the sphere of radius n is of order nα. We prove that in two dimensions, the growth exponent is strictly greater than one. The proof uses a known estimate on the third moment of the escape probability and an improvement on the discrete Beurling projection theorem. },
author = {Lawler, Gregory F.},
journal = {ESAIM: Probability and Statistics},
keywords = {loop-erased walk; Beurling projection theorem},
language = {eng},
month = {3},
pages = {1-21},
publisher = {EDP Sciences},
title = {A Lower Bound on the Growth Exponent for Loop-Erased Random Walk in Two Dimensions},
url = {http://eudml.org/doc/197727},
volume = {3},
year = {2010},
}

TY - JOUR
AU - Lawler, Gregory F.
TI - A Lower Bound on the Growth Exponent for Loop-Erased Random Walk in Two Dimensions
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 3
SP - 1
EP - 21
AB - The growth exponent α for loop-erased or Laplacian random walk on the integer lattice is defined by saying that the expected time to reach the sphere of radius n is of order nα. We prove that in two dimensions, the growth exponent is strictly greater than one. The proof uses a known estimate on the third moment of the escape probability and an improvement on the discrete Beurling projection theorem.
LA - eng
KW - loop-erased walk; Beurling projection theorem
UR - http://eudml.org/doc/197727
ER -

References

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