Discrete-time particle system with a wall and representations of O(infinity)

Details Discrete-time particle system with a wall and representations of O(infinity) Discrete-time particle system with a wall and representations of O(infinity)

2012-03-07

arxiv.org/abs/1203.1660v1

Mathematics

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14 pages

Scientific paper

We examine a discrete-time Markovian particle system on the quarter-plane introduced by M. Defosseux. The vertical boundary acts as a reflecting wall. We prove that on each horizontal level, it coincides with a Markov chain arising from a discrete family of representations of the infinite-dimensional orthogonal group. Both of these models lie in the Anisotropic Kardar-Parisi-Zhang universality class with a wall. For each fixed time and level, the particles form a determinantal point process. Using the formula for the correlation kernel, we take the large-time asymptotics and obtain the discrete Jacobi and symmetric Pearcey kernels. We also give a simple example which shows that in the multi-level case, the evolution of the two Markov chains is different.

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