Quantum Lunch: Geometry of random planar maps with high degrees – University of Copenhagen

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QMath > Events > Quantum Lunch > w 16 Budd

Quantum Lunch: Geometry of random planar maps with high degrees

Speaker: Timothy Budd, NBI.

Abstract: I will demonstrate how a peeling process can be used to explore the geometry of random planar maps, i.e. planar graphs embedded in the 2-sphere modulo homeomorphisms. When such random maps are fine-tuned to possess vertices of high degrees, we find deviations from typical scaling behavior, in particular in the growth of volumes and perimeters of geodesic balls. I'll discuss several consequences of this new scaling behavior, including (dependent on time) the recurrence vs. transience of random walks on these maps and the possibility of obtaining a new class of random continuum geometries arising in the scaling limit.

Based on arXiv:1602.01328.