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Integrable models for vicious and friendly walkers. (Russian, English) Zbl 1127.82023
Zap. Nauchn. Semin. POMI 335, 59-74 (2006); translation in J. Math. Sci., New York 143, No. 1, 2729-2737 (2007).
The author studies random walks of walkers on one-dimensional lattices and its connection with integrable models. It is considered two essentially different classes of random walkers: vicious and friendly. The walkers are called vicious since arriving on the same lattice site they annihilate not only one another but all the rest as well. On the contrary, the arbitrary number of the friendly walkers can share the same lattice sites. It is shown that the natural model describing the behavior of the friendly walkers is the integrable model of the boson type.

MSC:
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics
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