Markovian explorations of random planar maps are roundish

Understand

The infinite discrete stable Boltzmann maps are "heavy-tailed" generalisations of the well-known Uniform Infinite Planar Quadrangulation.

• Very efficient tools to study these objects are Markovian step-by-step explorations of the lattice called peeling processes.
• Such a process depends on an algorithm which selects at each step the next edge where the exploration continues.
• We prove here that, whatever this algorithm, a peeling process always reveals about the same portion of the map, thus growing roughly metric balls.