Geodesic
Geometry of Uniform Spanning Forest Components in High Dimensions
Canadian journal of mathematics, Tome 71 (2019) no. 6, pp. 1297-1321

Voir la notice de l'article provenant de la source Cambridge University Press

We study the geometry of the component of the origin in the uniform spanning forest of $\mathbb{Z}^{d}$ and give bounds on the size of balls in the intrinsic metric.
DOI : 10.4153/CJM-2017-054-x
Mots-clés : uniform spanning forest, loop-erased random walk 
Barlow, Martin T.; Járai, Antal A. Geometry of Uniform Spanning Forest Components in High Dimensions. Canadian journal of mathematics, Tome 71 (2019) no. 6, pp. 1297-1321. doi: 10.4153/CJM-2017-054-x
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     title = {Geometry of {Uniform} {Spanning} {Forest} {Components} in {High} {Dimensions}},
     journal = {Canadian journal of mathematics},
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     year = {2019},
     volume = {71},
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     doi = {10.4153/CJM-2017-054-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-054-x/}
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[AN] Aizenman, M. and Newman, C. M., Tree graph inequalities and critical behavior in percolation models . J. Stat. Phys. 36(1984), nos. 1/2, 107–143. . Google Scholar | DOI

[BM1] Barlow, M. T. and Masson, R., Exponential tail bounds for loop-erased random walk in two dimensions . Ann. Probab. 38(2010), no. 6, 2379–2417. . Google Scholar | DOI

[BM2] Barlow, M. T. and Masson, R., Spectral dimension and random walks on the two dimensional uniform spanning tree . Comm. Math. Phys. 305(2011), 23–57. . Google Scholar | DOI

[BLPS] Benjamini, I., Lyons, R., Peres, Y., and Schramm, O., Uniform spanning forests . Ann. Probab. 29(2001), 1–65. Google Scholar

[BHJ] Bhupatiraju, S., Hanson, J., and Járai, A. A., Inequalities for critical exponents in d-dimensional sandpiles . Electron. J. Probab. 22(2017), paper no. 85, 1–51. . Google Scholar | DOI

[La1] Lawler, Gregory F., A self-avoiding random walk . Duke Math. J. 47(1980), no. 3, 655–693. . Google Scholar | DOI

[La2] Lawler, Gregory F., Intersections of random walks . Probability and its Applications . Birkhäuser Boston, Boston, MA, 1991. Google Scholar

[La3] Lawler, Gregory F., The logarithmic correction for loop-erased walk in four dimensions . In: Proceedings of the Conference in Honor of Jean-Pierre Kahane . J. Fourier Anal. Appl. (1995) Special Issue, 347–361. Google Scholar

[Law99] Lawler, Gregory F., Loop-erased random walk . In: Perplexing problems in probability . Progress in probability, 44. Birkhäuser Boston, Boston, MA, 1999. Google Scholar

[LL] Lawler, Gregory F. and Limic, Vlada, Random walk: a modern introduction . Cambridge University Press, 2009. Google Scholar

[LMS] Lyons, R., Morris, B. J., and Schramm, O., Ends in uniform spanning forests . Electron. J. Probab. 13(2008), no. 58, 1702–1725. . Google Scholar | DOI

[LP] Lyons, R. and Peres, Y., Probability on trees and networks . Cambridge Series in Statistical and Probabilistic Mathematics, 42. Cambridge University Press, New York, 2016. Google Scholar

[Mas] Masson, Robert, The growth exponent for planar loop-erased random walk . Electron. J. Probab. 14(2009), no. 36, 1012–1073. . Google Scholar | DOI

[Pem91] Pemantle, R., Choosing a spanning tree for the integer lattice uniformly . Ann. Probab. 19(1991), no. 4, 1559–1574. . Google Scholar | DOI

[W] Wilson, D. B., Generating spanning trees more quickly than the cover time . Proceedings of the Twenty-eighth Annual ACM Symposium on the Theory of Computing . ACM, New York, 1996, pp. 296–303. Google Scholar

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