Directed Nonabelian Sandpile Models on Trees

Ayyer, Arvind and Schilling, Anne and Steinberg, Benjamin and Thiery, Nicolas M (2015) Directed Nonabelian Sandpile Models on Trees. In: COMMUNICATIONS IN MATHEMATICAL PHYSICS, 335 (3). pp. 1065-1098.

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Abstract

We define two general classes of nonabelian sandpile models on directed trees (or arborescences), as models of nonequilibrium statistical physics. Unlike usual applications of the well-known abelian sandpile model, these models have the property that sand grains can enter only through specified reservoirs. In the Trickle-down sandpile model, sand grains are allowed to move one at a time. For this model, we show that the stationary distribution is of product form. In the Landslide sandpile model, all the grains at a vertex topple at once, and here we prove formulas for all eigenvalues, their multiplicities, and the rate of convergence to stationarity. The proofs use wreath products and the representation theory of monoids.

Item Type:	Journal Article
Publication:	COMMUNICATIONS IN MATHEMATICAL PHYSICS
Publisher:	SPRINGER
Additional Information:	Copy right for this article belongs to the SPRINGER, 233 SPRING ST, NEW YORK, NY 10013 USA
Keywords:	SELF-ORGANIZED CRITICALITY; SEMIGROUP REPRESENTATION-THEORY; HYPERPLANE ARRANGEMENTS; MOBIUS FUNCTIONS; MARKOV-CHAINS; STEADY-STATE; RANDOM-WALKS; AUTOMATON; SPECTRUM; KINETICS
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	21 Apr 2015 07:59
Last Modified:	21 Apr 2015 07:59
URI:	http://eprints.iisc.ac.in/id/eprint/51350

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