Minimal configurations and sandpile measures
type: Item
instance of: scholarly article
title: Minimal configurations and sandpile measures
zbMATH Open document ID: 1307.60143
author: A. A. Járai
author: Nicolás Werning
published in: Journal of Theoretical Probability
publication date: 2014-09-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/1110.4523
full work available at URL: minimal arxiv 2.pdf
review text: Let \(G=(V\cup \{s\},E)\) be a finite connected multigraph, with a distinguished vertex \(s,\) called the sink. A sandpile on \(G\) is a configuration of particles on \(V\), specified by a map \(\eta:V\rightarrow \{0,1,2,\cdots \},\) where \(\eta(x)\) is the number of particles at \(x.\) The wired uniform spanning forest is a random spanning subgraph of \(G\) that is obtained, through a limiting process, from uniformly random spanning trees of finite graphs. The authors ``give a new simple construction of the sandpile measure on an infinite graph \(G\), under the sole assumption that each tree in the wired uniform spanning forest on \(G\) has one end almost surely'' and ``also give determinantal formulas for minimal configurations [\dots] in terms of the transfer current matrix'' (from authors' abstract).
reviewed by: Nasir N. Ganikhodjaev
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82C20
Mathematics Subject Classification ID: 05C80
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 6348419
zbMATH Keywords: Abelian sandpile
zbMATH Keywords: sandpile measure
zbMATH Keywords: finite connected multigraph
zbMATH Keywords: minimal configuration
zbMATH Keywords: uniform spanning tree
zbMATH Keywords: determinantal process
MaRDI profile type: Publication
OpenAlex ID: W1968966556
arXiv ID: 1110.4523
cites work: Infinite volume limit for the stationary distribution of Abelian sandpile models
cites work: Uniform spanning forests
cites work: Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances
cites work: Self-organized critical state of sandpile automaton models
cites work: Q3706275
cites work: Conformal covariance of the Abelian sandpile height one field
cites work: Chip-Firing and Rotor-Routing on Directed Graphs
cites work: Abelian sandpiles: an overview and results on certain transitive graphs
cites work: Ladder Sandpiles
cites work: Infinite volume limit of the abelian sandpile model in dimensions \(d \geq 3\)
cites work: Interplay of analysis and probability in physics. Abstracts from the workshop held January 22--28, 2012.
cites work: Random Walk: A Modern Introduction
cites work: The looping constant of \(\mathbb Z^d\)
cites work: Ends in uniform spanning forests
cites work: Probability on trees and networks
cites work: Coherent states for the hydrogen atom
cites work: Chip firing and the Tutte polynomial
cites work: Choosing a spanning tree for the integer lattice uniformly
cites work: Course 14 Mathematical aspects of the Abelian Sandpile model
DOI: 10.1007/S10959-012-0446-Z
description: scientific article; zbMATH DE number 6348419