TY - JOUR

T1 - Conditioned random walks and the RSK correspondence

AU - O'Connell, Neil

PY - 2003/3/28

Y1 - 2003/3/28

N2 - We consider the stochastic evolution of three variants of the RSK algorithm, giving both analytic descriptions and probabilistic interpretations. Symmetric functions play a key role, and the probabilistic interpretations are obtained by elementary Doob-Hunt theory. In each case, the evolution of the shape of the tableau obtained via the RSK algorithm can be interpreted as a conditioned random walk. This is intuitively appealing, and can be used for example to obtain certain relationships between orthogonal polynomial ensembles. In a certain scaling limit, there is a continous version of the RSK algorithm which inherits much of the structure exhibited in the discrete settings. Intertwining relationships between conditioned and unconditioned random walks are also given. In the continuous limit, these are related to the Harish-Chandra/Itzyksen-Zuber integral.

AB - We consider the stochastic evolution of three variants of the RSK algorithm, giving both analytic descriptions and probabilistic interpretations. Symmetric functions play a key role, and the probabilistic interpretations are obtained by elementary Doob-Hunt theory. In each case, the evolution of the shape of the tableau obtained via the RSK algorithm can be interpreted as a conditioned random walk. This is intuitively appealing, and can be used for example to obtain certain relationships between orthogonal polynomial ensembles. In a certain scaling limit, there is a continous version of the RSK algorithm which inherits much of the structure exhibited in the discrete settings. Intertwining relationships between conditioned and unconditioned random walks are also given. In the continuous limit, these are related to the Harish-Chandra/Itzyksen-Zuber integral.

UR - http://www.scopus.com/inward/record.url?scp=0037471292&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/36/12/312

DO - 10.1088/0305-4470/36/12/312

M3 - Article (Academic Journal)

AN - SCOPUS:0037471292

SN - 0305-4470

VL - 36

SP - 3049

EP - 3066

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 12 SPEC. ISS.

ER -