23 research outputs found
Exact formulas of the transition probabilities of the multi-species asymmetric simple exclusion process
We find the formulas of the transition probabilities of the -particle
multi-species asymmetric simple exclusion processes (ASEP), and show that the
transition probabilities are written as a determinant when the order of
particles in the final state is the same as the order of particles in the
initial state.Comment: 13 page
On the TASEP with Second Class Particles
In this paper we study some conditional probabilities for the totally
asymmetric simple exclusion processes (TASEP) with second class particles. To
be more specific, we consider a finite system with one first class particle and
second class particles, and we assume that the first class particle is
initially at the leftmost position. In this case, we find the probability that
the first class particle is at and it is still the leftmost particle at
time . In particular, we show that this probability is expressed by the
determinant of an matrix of contour integrals if the initial
positions of particles satisfy the step initial condition. The resulting
formula is very similar to a known formula in the (usual) TASEP with the step
initial condition which was used for asymptotics by Nagao and Sasamoto [Nuclear
Phys. B 699 (2004), 487-502]
Fredholm determinants in the multiparticle hopping asymmetric diffusion model
In this paper we treat the multiparticle hopping asymmetric diffusion model
(MADM) of which initial configuration is such that a single site is occupied by
infinitely many particles and all other sites are empty. We show that the
probability distribution of the leftmost particle's position
at time is represented by a Fredholm determinant. Also, we consider an
exclusion process type model of the MADM, which is the (two-sided) PushASEP.
For the PushASEP with the step Bernoulli initial condition, we find a Fredholm
determinant representation of the probability distribution of the
leftmost particle's position at