Analogue of Poisson type limit distribution in discrete bm-Fock space.

The analogue of ”Poisson type” limit distribution is constructed on the discrete bm-Fock space, which is a kind of ”Fock space” generated by all the increasing sequence in some countable, partially ordered set associated with positive symmetric cones in Euclidean spaces, including R_{d}^{+} , the Lorentz cone in Minkowski’s spacetime and the cone of positive definite real symmetric (d × d) matrices. The Analysis of the cones plays significant role in our study and the combinatorics is based on bm-ordered noncrossing partitions with blocks consisting of either one or two elements.