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\(XXO\) Heisenberg chain and random walks. (Russian, English) Zbl 1080.60090
Zap. Nauchn. Semin. POMI 325, 13-27 (2005); translation in J. Math. Sci., New York 138, No. 3, 5636-5643 (2006).
The author shows that one can consider the time-dependent correlation functions of the \( XXO \) Heisenberg chain as the generating functions of random walks on a one-dimensional lattice. The explicit forms of correlation functions on infinite, semi-infinite and finite lattices are obtained. The long time asymptotic behaviour of these functions is studied.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
05E10 Combinatorial aspects of representation theory
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
60G50 Sums of independent random variables; random walks
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