Random Walks, Electric Networks and The Transience Class problem of Sandpiles

zbMath1423.05157arXiv1105.3368MaRDI QIDQ5743503

Sundar Vishwanathan, Ayush Choure

Publication date: 10 May 2019

Full work available at URL: https://arxiv.org/abs/1105.3368

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Applications of graph theory to circuits and networks (94C15) Random walks on graphs (05C81)

Related Items (1)

On graph parameters guaranteeing fast sandpile diffusion

Cites Work

• Chip-firing games on graphs
• On the sandpile group of the square cycle \(C^{2}_{n}\)
• On the sandpile group of regular trees
• On the sandpile group of \(3\times n\) twisted bracelets
• Games on line graphs and sand piles
• Chip-firing and the critical group of a graph
• Harmonic and analytic functions on graphs
• On the sandpile group of dual graphs
• Goldbug variations
• On the sandpile group of the graph \(K_{3}\times C_n\)
• The art of random walks.
• The computational complexity of one-dimensional sandpiles
• Almost tight bounds for rumour spreading with conductance
• Polynomial Bound for a Chip Firing Game on Graphs
• Self-organized critical state of sandpile automaton models
• Algebraic aspects of Abelian sandpile models
• Faster Generation of Random Spanning Trees
• Electrical flows, laplacian systems, and faster approximation of maximum flow in undirected graphs
• Expander flows, geometric embeddings and graph partitioning
• The structure of a linear chip firing game and related models
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