Infinite stable Boltzmann planar maps are subdiffusive - Archive ouverte HAL Access content directly
Journal Articles Probability and Mathematical Physics Year : 2021

Infinite stable Boltzmann planar maps are subdiffusive

(1) ,
1
Cyril Marzouk

Abstract

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

Dates and versions

hal-03287273 , version 1 (15-07-2021)

Identifiers

Cite

Nicolas Curien, Cyril Marzouk. Infinite stable Boltzmann planar maps are subdiffusive. Probability and Mathematical Physics, 2021. ⟨hal-03287273⟩
21 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More