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In this paper, a group shift is an expansive action of Zd on a compact metrizable zero dimensional group by continuous automorphisms. All group shifts factor topologically onto equal-entropy Bernoulli...
Zd SHIFTS OF FINITE TYPE WITHOUT EQUAL ENTROPY FULL SHIFT FACTORS
Zd SHIFTS FINITE TYPE ENTROPY FULL SHIFT
2015/9/29
For d ≥ 2, we use results of Hochman and Meyerovitch to construct examples of Zd shifts of finite type of entropy log N, N ∈ N, which cannot factor topologically onto the Zd Bernoulli shift on N symbo...
Spherical Asymptotics for the Rotor-Router Model in Zd
Spherical Asymptotics Rotor-Router Model Zd
2015/8/14
The rotor-router model is a deterministic analogue of random walk invented by Jim Propp. It can be used to definea deterministic aggregation model analogous to internal diffusion limited aggregation. ...
Rotor walk is a deterministic analogue of random walk. We study its recurrence and transience properties on Zd for the initial configuration of all rotors aligned. If n particles in turn perform rotor...
THE LOOPING CONSTANT OF Zd
LOOPING CONSTANT Zd
2015/8/14
The looping constant ξ(Zd) is the expected number of neighbors of the origin that lie on the infinite loop-erased random walk in Zd.Poghosyan, Priezzhev and Ruelle, and independently, Kenyon and Wilso...