Pair-factorized steady states on arbitrary graphs
arXiv:0904.0355 · doi:10.1088/1751-8113/42/31/315003
Abstract
Stochastic mass transport models are usually described by specifying hopping rates of particles between sites of a given lattice, and the goal is to predict the existence and properties of the steady state. Here we ask the reverse question: given a stationary state that factorizes over links (pairs of sites) of an arbitrary connected graph, what are possible hopping rates that converge to this state? We define a class of hopping functions which lead to the same steady state and guarantee current conservation but may differ by the induced current strength. For the special case of anisotropic hopping in two dimensions we discuss some aspects of the phase structure. We also show how this case can be traced back to an effective zero-range process in one dimension which is solvable for a large class of hopping functions.
IOP style, 9 pages, 1 figure
References in corpus (5)
Cited by in corpus (10)
- Mass condensation in one dimension with pair-factorized steady states
- Structure of the condensed phase in the inclusion process
- Cluster-factorized steady states in finite range processes
- Zero-range process with finite compartments: Gentile's statistics and glassiness
- Poisson-Dirichlet asymptotics in condensing particle systems
- Emergence of dynamic phases in the presence of different kinds of open boundaries in stochastic transport with short-range interactions
- The validity of the no-pumping theorem in systems with finite-range interactions between particles
- A simple non-equilibrium, statistical-physics toy model of thin-film growth
- Condensation transition in a conserved generalized interacting zero-range process
- Particle hopping on a ladder: exact solution using multibalance