Invariant measures and limiting shapes in sandpile models
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چکیده
منابع مشابه
Sandpile models : The infinite volume model , Zhang ’ s model and limiting shapes
We define stabilizability of an infinite volume height configuration and of a probability measure on height configurations. We show that for high enough densities, a probability measure cannot be stabilized. We also show that in some sense the thermodynamic limit of the uniform measures on the recurrent configurations of the abelian sandpile model (ASM) is a maximal element of the set of stabil...
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We study the rotor router model and two deterministic sandpile models. For the rotor router model in Z, Levine and Peres proved that the limiting shape of the growth cluster is a sphere. For the other two models, only bounds in dimension 2 are known. A unified approach for these models with a new parameter h (the initial number of particles at each site), allows to prove a number of new limitin...
متن کاملLimiting Shapes for a Non-Abelian Sandpile Growth Model and Related 353 Cellular Automata
We present limiting shape results for a non-abelian variant of the abelian sandpile growth model (ASGM), some of which have no analog in the ASGM. One of our limiting shapes is an octagon. In our model, mass spreads from the origin by the toppling rule in Zhang’s sandpile model. Previously, several limiting shape results have been obtained for the ASGM using abelianness and monotonicity as main...
متن کاملLimiting Shapes for a Non-abelian Sandpile Growth Model and Related Cellular Automata
We present limiting shape results for a non-abelian variant of the abelian sandpile growth model (ASGM), some of which have no parallel in the ASGM. One of our limiting shapes is an octagon. In our model, mass spreads from the origin by the toppling rule in Zhang’s sandpile model. Previously, several limiting shape results have been obtained for the ASGM using abelianness and monotonicity as ma...
متن کاملDirect evidence for conformal invariance of avalanche frontiers in sandpile models.
Appreciation of stochastic Loewner evolution (SLE_{kappa}) , as a powerful tool to check for conformal invariant properties of geometrical features of critical systems has been rising. In this paper we use this method to check conformal invariance in sandpile models. Avalanche frontiers in Abelian sandpile model are numerically shown to be conformally invariant and can be described by SLE with ...
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تاریخ انتشار 2010