Markovian explorations of random planar maps are roundish
| Autor: | Cyril Marzouk, Nicolas Curien |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques d'Orsay (LMO), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), European Project: ERC-2016-STG 716083,CombiTop, European Project, Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2019 |
| Předmět: |
Computer science
General Mathematics 010102 general mathematics Probability (math.PR) Markov process 16. Peace & justice Simple random sample 01 natural sciences [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 010104 statistics & probability symbols.namesake Planar Lattice (order) Boltzmann constant symbols FOS: Mathematics 0101 mathematics Algorithm Mathematics - Probability |
| Zdroj: | Bulletin de la société mathématique de France Bulletin de la société mathématique de France, Société Mathématique de France, 2020, 148 (4), pp.709-732. ⟨10.24033/bsmf.2821⟩ Bulletin de la société mathématique de France, 2020, 148 (4), pp.709-732. ⟨10.24033/bsmf.2821⟩ Bulletin de la Société mathématique de France |
| ISSN: | 0037-9484 1777-568X 2102-622X |
| DOI: | 10.48550/arxiv.1902.10624 |
| Popis: | 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. Applied to well-designed algorithms, this easily enables us to compare distances in the map and in its dual, as well as to control the so-called pioneer points of the simple random walk, both on the map and on its dual. Comment: 17 pages, 3 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|