Return to Colloquia & Seminar listing
Integral Formulas for the Asymmetric Simple Exclusion Process
Probability| Speaker: | Craig Tracy, UC Davis |
| Location: | 1147 MSB |
| Start time: | Wed, May 9 2007, 3:10PM |
Description
In this paper we obtain general integral formulas for probabilities in the
asymmetric simple exclusion process (ASEP) on the integer lattice Z with nearest
neighbor hopping rates p to the right and q = 1−p to the left. For the most
part we consider an N-particle system but for certain of these formulas we can
take the N → ∞ limit. First we obtain, for the N-particle system, a formula for
the probability of a configuration at time t, given the initial configuration. For
this we use Bethe Ansatz ideas to solve the master equation, extending a result
of Sch¨utz for the case N = 2. The main results of the paper, derived from
this, are integral formulas for the probability, for given initial configuration,
that the mth left-most particle is at x at time t. In one of these formulas we
can take the N → ∞ limit, and it gives the probability for an infinite system
where the initial configuration is bounded on one side. For the special case of
the totally asymmetric simple exclusion process (TASEP) our formulas reduce
to the known ones