--- res: bibo_abstract: - We use methods from combinatorics and algebraic statistics to study analogues of birth-and-death processes that have as their state space a finite subset of the m-dimensional lattice and for which the m matrices that record the transition probabilities in each of the lattice directions commute pairwise. One reason such processes are of interest is that the transition matrix is straightforward to diagonalize, and hence it is easy to compute n step transition probabilities. The set of commuting birth-and-death processes decomposes as a union of toric varieties, with the main component being the closure of all processes whose nearest neighbor transition probabilities are positive. We exhibit an explicit monomial parametrization for this main component, and we explore the boundary components using primary decomposition.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Steven foaf_name: Evans, Steven N foaf_surname: Evans - foaf_Person: foaf_givenName: Bernd foaf_name: Sturmfels, Bernd foaf_surname: Sturmfels - foaf_Person: foaf_givenName: Caroline foaf_name: Caroline Uhler foaf_surname: Uhler foaf_workInfoHomepage: http://www.librecat.org/personId=49ADD78E-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-7008-0216 bibo_doi: 10.1214/09-AAP615 bibo_volume: 20 dct_date: 2010^xs_gYear dct_publisher: Institute of Mathematical Statistics@ dct_title: Commuting birth and death processes@ ...