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Linear bounds on the North-East model and higher-dimensional analogs. (English) Zbl 1126.82307

Summary: The North-East model is a combinatorial model arising from statistical physics in which counters are placed at or removed from lattice points in a quadrant, according to certain rules, while bounding the total number of occupied sites. We show that any site may be reached with a number of counters linear in the distance of the site from the origin. We also show that in contrast with the one-dimensional East model, a linear number of counters is necessary. We extend the North-East model to n dimensions with corresponding linear upper and lower bounds. In two dimensions, a polynomial number of steps are sufficient to achieve the linear upper bound.

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
05A16 Asymptotic enumeration
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
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