| Issue |
ESAIM: Proc.
Volume 51, October 2015
Modélisation Aléatoire et Statistique - Journées MAS 2014
|
|
|---|---|---|
| Page(s) | 60 - 73 | |
| DOI | https://doi.org/10.1051/proc/201551004 | |
| Published online | 12 October 2015 | |
Learning about critical phenomena from scribbles and sandpiles*
ETH, Departement Mathematik, Rämistrasse 101, 8092 Zürich,
Switzerland ;
adrien.kassel@math.ethz.ch
This text grew out of the notes for a talk given at the Journées MAS 2014. We give a concise report on our recent work on loop-erased random walk and related processes (spanning trees, cycle-rooted spanning forests, and sandpiles) on planar lattices and on graphs embedded in Riemannian surfaces in the limit of small meshsize.
Résumé
Ce texte est issu des notes d’un exposé donné aux Journées MAS 2014. Nous présentons une synthèse de nos travaux récents sur la marche aléatoire à boucles effacées et certains processus reliés (tels les arbres couvrants, les forêts couvrantes d’unicycles, le tas de sable abélien) sur les réseaux planaires et sur les graphes plongés dans les surfaces riemanniennes dans la limite où la maille tend vers zéro.
The author acknowledges the hospitality of ENS Paris, Brown University, MSRI in Berkeley, Microsoft Research Redmond, and Université Paris Sud. Principal support was provided by a French doctoral grant. Additional support was provided by the Fulbright Foundation and the Fondation Sciences Mathématiques de Paris
© EDP Sciences, SMAI 2015
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