Laplacian growth, sandpiles, and scaling limits

DOI10.1090/bull/1573zbMath1451.37013arXiv1611.00411OpenAlexW2546535094MaRDI QIDQ5122445

Lionel Levine, Yuval Peres

Publication date: 22 September 2020

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.00411

zbMATH Keywords

scaling limitobstacle problemdiscrete Laplacianinternal diffusion limited aggregationchip-firingrotor-router modeldivisible sandpileunicycleabelian sandpileeulerian walkerslooping constantTutte slope

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Free boundary problems for PDEs (35R35) Discrete potential theory (31C20) Dynamical aspects of statistical mechanics (37A60) Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics (82C24) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

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Laplacian growth and sandpiles on the Sierpiński gasket: limit shape universality and exact solutions, A shape theorem for exploding sandpiles, Existence of a phase transition in harmonic activation and transport, Asymptotic height distribution in high-dimensional sandpiles, Constructing fractional Gaussian fields from long-range divisible sandpiles on the torus, Characterizing immutable sandpiles: a first look, Perturbed divisible sandpiles and quadrature surfaces, Sandpile models, DIVISIBLE SANDPILE ON SIERPINSKI GASKET GRAPHS, Non-Archimedean Coulomb gases, Sandpile toppling on Penrose tilings: identity and isotropic dynamics, Dynamic dimensional reduction in the abelian sandpile

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