Geodesic
UNIFORM SPANNING FORESTS OF PLANAR GRAPHS
Forum of Mathematics, Sigma, Tome 7 (2019)

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

We prove that the free uniform spanning forest of any bounded degree proper plane graph is connected almost surely, answering a question of Benjamini, Lyons, Peres and Schramm. We provide a quantitative form of this result, calculating the critical exponents governing the geometry of the uniform spanning forests of transient proper plane graphs with bounded degrees and codegrees. We find that the same exponents hold universally over this entire class of graphs provided that measurements are made using the hyperbolic geometry of their circle packings rather than their usual combinatorial geometry. 
@article{10_1017_fms_2019_14,
     author = {TOM HUTCHCROFT and ASAF NACHMIAS},
     title = {UNIFORM {SPANNING} {FORESTS} {OF} {PLANAR} {GRAPHS}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {7},
     year = {2019},
     doi = {10.1017/fms.2019.14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2019.14/}
}
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TOM HUTCHCROFT; ASAF NACHMIAS. UNIFORM SPANNING FORESTS OF PLANAR GRAPHS. Forum of Mathematics, Sigma, Tome 7 (2019). doi: 10.1017/fms.2019.14

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