Kenyon, Richard Long-range properties of spanning trees. (English) Zbl 0977.82011 J. Math. Phys. 41, No. 3, 1338-1363 (2000). Summary: We compute some large-scale properties of the uniform spanning tree process on bounded regions in \(\mathbb{Z}^2\). In particular, we compute the distribution of the meeting point of the branches of the tree issued from three boundary points. We also compute the crossing probabilities of branches of the tree on rectangular and annular regions, as well as the winding number of the branches of the tree. Cited in 20 Documents MSC: 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B05 Classical equilibrium statistical mechanics (general) Keywords:uniform spanning tree; conformal invariance; crossing probabilities; winding number PDFBibTeX XMLCite \textit{R. Kenyon}, J. Math. Phys. 41, No. 3, 1338--1363 (2000; Zbl 0977.82011) Full Text: DOI Link References: [1] Pemantle R., Ann. Prob. 19 pp 1559– (1991) · Zbl 0758.60010 · doi:10.1214/aop/1176990223 [2] Burton R., Ann. Prob. 21 pp 1329– (1993) · Zbl 0785.60007 · doi:10.1214/aop/1176989121 [3] Duplantier B., J. Stat. Phys. 49 pp 411– (1987) · doi:10.1007/BF01009343 [4] Kenyon R., Ann. Inst. Henri Poincaré 33 pp 591– (1997) · Zbl 0893.60047 · doi:10.1016/S0246-0203(97)80106-9 [5] Percus J. K., J. Math. Phys. 10 pp 1881– (1969) · doi:10.1063/1.1664774 [6] Kasteleyn P. W., Physica (Amsterdam) 27 pp 1209– (1961) · Zbl 1244.82014 · doi:10.1016/0031-8914(61)90063-5 [7] Duplantier B., J. Stat. Phys. 51 pp 327– (1988) · Zbl 1086.82501 · doi:10.1007/BF01028464 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.