2012/04/05 by Tomohiro Sasamoto, Lauren Williams, Sasamoto, Tomohiro +1 · 1 citation
Mathematics · Physics and Astronomy · #05E10 #60C05 #82B23 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #math-ph #math.CO #math.MP #math.PR #msc:05E10 #msc:60C05 #msc:82B23
paper · pdf · doi:10.48550/arxiv.1204.1114
arxiv created 2012/04/05 · arxiv updated 2012/04/06
We study two versions of the asymmetric exclusion process (ASEP) -- an ASEP on a semi-infinite lattice with an open left boundary, and an ASEP on a finite lattice with open left and right boundaries -- and we demonstrate a surprising relationship between their stationary measures. The semi-infinite ASEP was first studied by Liggett and then Grosskinsky, while the finite ASEP had been introduced earlier by Spitzer and Macdonald-Gibbs-Pipkin. We show that the finite correlation functions involving the first L sites for the stationary measures on the semi-infinite ASEP can be obtained as a nonphysical specialization of the stationary distribution of an ASEP on a finite one-dimensional lattice with L sites. Namely, if the output and input rates of particles at the right boundary of the finite ASEP are beta and delta, respectively, and we set delta=-beta, then this specialization corresponds to sending the right boundary of the lattice to infinity. Combining this observation with work of the second author and Corteel, we obtain a combinatorial formula for finite correlation functions of the ASEP on a semi-infinite lattice.