A lower bound on the growth exponent for loop-erased random walk in two dimensions
ESAIM: Probability and Statistics, Tome 3 (1999), pp. 1-21. 
@article{PS_1999__3__1_0,
     author = {Lawler, Gregory F.},
     title = {A lower bound on the growth exponent for loop-erased random walk in two dimensions},
     journal = {ESAIM: Probability and Statistics},
     pages = {1--21},
     publisher = {EDP-Sciences},
     volume = {3},
     year = {1999},
     mrnumber = {1694205},
     zbl = {0926.60041},
     language = {en},
     url = {http://archive.numdam.org/item/PS_1999__3__1_0/}
}
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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, Tome 3 (1999), pp. 1-21. http://archive.numdam.org/item/PS_1999__3__1_0/

[1] Ahlfors L., Conformal Invariance. Topics in Geometric Function Theory. McGraw-Hill ( 1973). | MR | Zbl

[2] Billingsley P., Probability and Measure. 2nd ed., John Wiley ( 1986). | MR | Zbl

[3] Burdzy K. and Lawler G., Rigorous exponent inequalities for random walks. J. Phys. A. 2 3 ( 1990) L23-L28. | MR | Zbl

[4] Duplantier B., Loop-erased self-avoiding walks in 2D. Physica A 191 ( 1992) 516-522.

[5] Fargason C., The percolation dimension of Brownian motion in three dimensions. Ph.D. dissertation, Duke University ( 1998).

[6] Guttmann A. and Bursill R., Critical exponent for the loop-erased self-avoiding walk by Monte Carlo methods. J. Stat. Phys. 59 ( 1990) 1-9.

[7] Kenyon R., The asymptotic distribution of the discrete Laplacian ( 1998) preprint.

[8] Kesten H., Hitting probabilities of random walks on ℤd. Stoc. Proc. Appl. 25 ( 1987) 165-184. | MR | Zbl

[9] Lawler G., Intersections of Random Walks. Birkhäuser-Boston ( 1991). | MR | Zbl

[10] Lawler G., A discrete analogue of a theorem of Makarov. Comb. Prob. Computing 2 ( 1993) 181-199. | MR | Zbl

[11] Lawler G., The logarithmic correction for loop-erased walk in four dimensions, Proceedings of the Conference in Honor of Jean-Pierre Kahane (Orsay 1993), special issue of J. Fourier Anal. Appl. ( 1995) 347-362. | MR | Zbl

[12] Lawler G., Cut points for simple random walk. Electron. J. Prob. 1 ( 1996) 13. | EuDML | MR | Zbl

[13] Lawler G., Loop-erased random walk, preprint, to appear in volume in honor of Harry Kesten ( 1998). | MR | Zbl

[14] Lawler G. and Puckette E., The intersection exponent for simple random walk ( 1998) preprint. | MR | Zbl

[15] Madras N. and Slade G., The Self-Avoiding Walk. Birkhäuser-Boston ( 1993). | MR | Zbl

[16] Majumdar S.N., Exact fractal dimension of the loop-erased self-avoiding random walk in two dimensions, Phys. Rev. Lett. 68 ( 1992) 2329-2331.

[17] Pemantle R., Choosing a spanning tree for the integer lattice uniformly. Ann. Prob. 19 ( 1991) 1559-1574. | MR | Zbl

[18] Propp J. and Wilson D., How to get a perfectly random sample from a generic Markov chain and generate a random spanning tree of a directed graph. J. Algorithms (to appear). | MR | Zbl

[19] Pommerenke C., Boundary Behaviour of Conformal Maps, Springer-Verlag ( 1992). | MR | Zbl

[20] Werner W., Beurling's projection theorem via one-dimensional Brownian motion. Math. Proc. Cambridge Phil. Soc. 119 ( 1996) 729-738. | MR | Zbl