Sandpiles
Home Sage Algebraic Geometry Applets/Java Gallery	Literature Links to miscellaneous papers I find interesting: Holroyd, Levine, Meszaros, Peres, Propp, Wilson Chip-Firing and Rotor-Routing on Directed Graphs. The final version of this paper appears in In and out of Equilibrium II, Eds. V. Sidoravicius, M. E. Vares, in the Series Progress in Probability, Birkhauser (2008). This is my recommendation for an introduction to the subject (along with Babai's notes and Dhar's 2006 paper referenced below). L. Levine Sandpile groups and spanning trees of directed line graphs. Parallel Chip-Firing on the Complete Graph: Devil's Staircase and Poincare Rotation Number. Driving sandpiles to criticality and beyond. D. Dhar Exactly Solved Models of Self-Organized Criticality, Physica A 369 (2006). The abelian sandpile and related models, Physica A 263 (1999). Algebraic Aspects of Abelian Sandpile Models, TIFR/TH/94-30. M. Baker Riemann-Roch and Abel-Jacobi Theory on a Finite Graph, with Serguei Norine, Advances in Mathematics 215 (2007), 766--788. Specialization of Linear Systems from Curves to Graphs, Algebra & Number Theory 2, no. 6 (2008), 613--653. Harmonic Morphisms and Hyperelliptic Graphs, with Serguei Norine, (2008). Gathmann, Kerber A Riemann-Roch theorem in tropical geometry, (2007). Haase, Musiker, Yu Linear Systems on Tropical Curves. J. Ellis-Monaghan and C. Merino Graph polynomials and their applications I: The Tutte polynomial, (2008). Graph polynomials and their applications II: Interrelations and interpretations, (2008). Cori, Rossin, Salvy Polynomial Ideals for Sandpiles and their Grobner Bases, INRIA (2000). Babai's 2005 REU lecture notes on sandpiles. E. Speer Asymmetric Abelian sandpile models, preprint of paper in J. Stat. Phys. 71 (1993), 61-74. This paper contains a generalization of Dhar's burning algorithm to directed graphs. Jaeger group in granular physics at the University of Chicago Abstracts. Homepage. Movies of sand behaving as a liquid.

Sandpiles

Literature

Links to miscellaneous papers I find interesting:

Holroyd, Levine, Meszaros, Peres, Propp, Wilson
- Chip-Firing and Rotor-Routing on Directed Graphs. The final version of this paper appears in In and out of Equilibrium II, Eds. V. Sidoravicius, M. E. Vares, in the Series Progress in Probability, Birkhauser (2008). This is my recommendation for an introduction to the subject (along with Babai's notes and Dhar's 2006 paper referenced below).
L. Levine
D. Dhar
- Exactly Solved Models of Self-Organized Criticality, Physica A 369 (2006).
- The abelian sandpile and related models, Physica A 263 (1999).
- Algebraic Aspects of Abelian Sandpile Models, TIFR/TH/94-30.
M. Baker
- Riemann-Roch and Abel-Jacobi Theory on a Finite Graph, with Serguei Norine, Advances in Mathematics 215 (2007), 766--788.
- Specialization of Linear Systems from Curves to Graphs, Algebra & Number Theory 2, no. 6 (2008), 613--653.
- Harmonic Morphisms and Hyperelliptic Graphs, with Serguei Norine, (2008).
Gathmann, Kerber
- A Riemann-Roch theorem in tropical geometry, (2007).
Haase, Musiker, Yu
- Linear Systems on Tropical Curves.
J. Ellis-Monaghan and C. Merino
- Graph polynomials and their applications I: The Tutte polynomial, (2008).
- Graph polynomials and their applications II: Interrelations and interpretations, (2008).
Cori, Rossin, Salvy
- Polynomial Ideals for Sandpiles and their Grobner Bases, INRIA (2000).
Babai's 2005 REU lecture notes on sandpiles.
E. Speer
- Asymmetric Abelian sandpile models, preprint of paper in J. Stat. Phys. 71 (1993), 61-74. This paper contains a generalization of Dhar's burning algorithm to directed graphs.
Jaeger group in granular physics at the University of Chicago
- Abstracts.
- Homepage.
- Movies of sand behaving as a liquid.