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We consider a multilevel continuous time Markov chain $X(s;N) = (X_i^j(s;N):1 \leq i \leq j \leq N)$, which is defined by means of Jack symmetric functionsand forms a certain discretization of the multilevel Dyson Brownian motion. Theprocess $X(s;N)$ describes the evolution of a discrete interlacing particlesystem with push-block interactions between the particles, which preserve theinterlacing property. We study the joint asymptotic separation of the particlesat the right edge of the ensemble as the number of levels and time tend toinfinity and show that the limit is described by a certain zero range processwith local interactions.

Interacting particle systems at the edge of multilevel Jack processes