Fetching the paper…
Reading the bibliography…
We show that the transition probability of the Markoc chain $(G(j,1),...,G(j,n))_{j\ge 1}$, where the $G(i,j)'s$ are certain directed last-passage times, is given by a determinant of a special form.
G. M. Schütz, Exact Solution of the Master Equation for the Asymmetric Exclusion Process,
1997
Earlier work this paper cites.
A. Borodin, A. Okounkov & G. Olshanski, Asymptotics of Plancherel measures for symmetric groups,
2000
Earlier work this paper cites.
K. Johansson, Shape fluctuations and random matrices,
2000
Earlier work this paper cites.
Yu. Baryshnikov, GUES and QUEUES,
2001
Earlier work this paper cites.
K. Johansson, Discrete orthogonal polynomial ensembles and the Plancherel measure,
2001
Earlier work this paper cites.
A. Okounkov, Infinite wedge and random partitions,
2001
Cited alongside, same era.
J. Gravner, C. A. Tracy, H. Widom, A growth model in a random environment,
2002
Cited alongside, same era.
K. Johansson, Discrete polynuclear growth and determinantal processes,
2003
Cited alongside, same era.
J. G. Brankov, V. B. Priezzhev, R. V. Shelest, Genneralized determinant solution of the discrete-time totally asymmetric exclusion process and zero-range process,
2004
Cited alongside, same era.
T. Nagao, T. Sasamoto, Asymmetric Simple Exclusion Process and Modified Random Matrix Ensembles,
2004
Cited alongside, same era.
A. B. Dieter, J. Warren, Transition probabilities, queues in series and determinants,
Cited in the paper.
R. Koekoek, R.F. Swarttouw, The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
Cited in the paper.
C. Krattenthaler, Advanced Determinant Calculus
Cited in the paper.
C. A. Tracy, H. Widom, Integral formulas for the asymmetric simple exclusion process,
Cited in the paper.
K. Johansson, Random Matrices and determinantal processes,
2005
Later among the works it cites.
A. Rákos and G.M. Schütz, Current distribution and Random Matrix Ensembles for an Integrable Asymmetric Fragmentation Process,
2005
Later among the works it cites.
A. Borodin & G. Olshanski, Stochastic dynamics related to Plancherel measure on partitions,
2006
Later among the works it cites.
J. Warren, Dyson’s Brownian motions, intertwing and interlacing,
2007
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…