Garban, Christophe; Pete, Gábor; Schramm, Oded The scaling limits of the minimal spanning tree and invasion percolation in the plane. (English) Zbl 1426.60117 Ann. Probab. 46, No. 6, 3501-3557 (2018). Summary: We prove that the Minimal Spanning Tree and the Invasion Percolation Tree on a version of the triangular lattice in the complex plane have unique scaling limits, which are invariant under rotations, scalings, and, in the case of the \(\mathsf{MST}\), also under translations. However, they are not expected to be conformally invariant. We also prove some geometric properties of the limiting \(\mathsf{MST}\). The topology of convergence is the space of spanning trees introduced by M. Aizenman et al. [Random Struct. Algorithms 15, No. 3–4, 319–367 (1999; Zbl 0939.60031)], and the proof relies on the existence and conformal covariance of the scaling limit of the near-critical percolation ensemble, established in our earlier works. Cited in 7 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B27 Critical phenomena in equilibrium statistical mechanics 82B43 Percolation 05C05 Trees 60D05 Geometric probability and stochastic geometry 81T27 Continuum limits in quantum field theory 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics Keywords:minimal spanning tree; invasion percolation; critical and near-critical percolation; scaling limit; conformal invariance; Hausdorff dimension Citations:Zbl 0939.60031 PDFBibTeX XMLCite \textit{C. Garban} et al., Ann. Probab. 46, No. 6, 3501--3557 (2018; Zbl 1426.60117) Full Text: DOI arXiv Euclid References: [1] Addario-Berry, L., Broutin, N. and Goldschmidt, C. (2012). The continuum limit of critical random graphs. Probab. Theory Related Fields152 367–406. · Zbl 1239.05165 [2] Addario-Berry, L., Broutin, N., Goldschmidt, C. and Miermont, G. (2017). 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