1,390 research outputs found
Combinatorics of the asymmetric exclusion process on a semi-infinite lattice
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
A systematic way to find and construct exact finite dimensional matrix product stationary states
We explain how to construct matrix product stationary states which are
composed of finite-dimensional matrices. Our construction explained in this
article was first presented in a part of [Hieida and Sasamoto:J. Phys. A: Math.
Gen. 37 (2004) 9873] for general models. In this article, we give more details
on the treatment than in the above-mentioned reference, for one-dimensional
asymmetric simple exclusion process(ASEP).Comment: This article will appear in the proceedings of "Workshop on Matrix
Product State Formulation and Density Matrix Renormalization Group
Simulations (MPS&DMRG)" to be published by World Scientifi
Fluctuations of a one-dimensional polynuclear growth model in a half space
We consider the multi-point equal time height fluctuations of a
one-dimensional polynuclear growth model in a half space. For special values of
the nucleation rate at the origin, the multi-layer version of the model is
reduced to a determinantal process, for which the asymptotics can be analyzed.
In the scaling limit, the fluctuations near the origin are shown to be
equivalent to those of the largest eigenvalue of the orthogonal/symplectic to
unitary transition ensemble at soft edge in random matrix theory.Comment: 51 pages, 8 figure
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