Form factors, plane partitions and random walks

An exactly solvable boson model, the so-called “phase model,” is considered. A relation between certain transition matrix elements of this model and boxed plane partitions, three-dimensional Young diagrams placed into a box of finite size, is established. It is shown that the natural model describing the behavior of friendly walkers, ones that can share the same lattice sites, is the “phase model.” An expression for the number of all admissible nests of lattice paths made by a fixed number of friendly walkers for a certain number of steps is obtained. Bibl. – 35 titles.