Description
Part 2 focuses on sandpiles, which are toy models of physical systems with dynamics controlled by the discrete Laplacian of the underlying graph. The text provides a careful introduction to the sandpile group and the abelian sandpile model, leading ultimately to L. Levine's threshold density theorem for the fixed-energy sandpile Markov chain. In a precise sense, the theory of sandpiles is dual to the theory of divisors, and there are many beautiful connections between the first two parts of the book.
Part 3 addresses various topics connecting the theory of chip-firing to other areas of mathematics, including the matrix-tree theorem, harmonic morphisms, parking functions, $M$-matrices, matroids, the Tutte polynomial, and simplicial homology. The text is suitable for advanced undergraduates and beginning graduate students.
About the Author
Scott Corry, Lawrence University, Appleton, WI.
David Perkinson, Reed College, Portland, OR.
Book Information
ISBN 9781470442187
Author Scott Corry
Format Paperback
Page Count 329
Imprint American Mathematical Society
Publisher American Mathematical Society
Weight(grams) 609g