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

ESAIM: Probability and Statistics (2010)

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

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topLawler, 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 -

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