Department of Mathematics
Blocks in the asymmetric simple exclusion process
- Author(s): Tracy, CA
- Widom, H
- et al.
Published Web Locationhttps://doi.org/10.1063/1.4996345
© 2017 Author(s). In earlier work, the authors obtained formulas for the probability in the asymmetric simple exclusion process that the mth particle from the left is at site x at time t. They were expressed in general as sums of multiple integrals and, for the case of step initial condition, as an integral involving a Fredholm determinant. In the present work, these results are generalized to the case where the mth particle is the left-most one in a contiguous block of L particles. The earlier work depended in a crucial way on two combinatorial identities, and the present work begins with a generalization of these identities to general L.