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The infinite discrete stable Boltzmann maps are generalisations of thewell-known Uniform Infinite Planar Quadrangulation in the case where largedegree faces are allowed. We show that the simple random walk on these randomlattices is always subdiffusive with exponent less than 1/3. Our method isbased on stationarity and geometric estimates obtained via the peeling processwhich are of own interest.

Infinite stable Boltzmann planar maps are subdiffusive