2017/07/24 by Craig A. Tracy, Harold Widom · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP
paper · pdf · doi:10.1063/1.4996345
published as Journal of Mathematical Physics 58, 123302 (2017) · 17 pages. Version 2 elaborates on a point overlooked in Version 1
arxiv created 2017/07/24 · arxiv updated 2017/12/22
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.