Reverse juggling processes

Abstract

Knutson introduced two families of reverse juggling Markov chains (single and multispecies) motivated by the study of random semi-infinite matrices over ${\mathbb{F}}_q$. We present natural generalizations of both chains by placing generic weights that still lead to simple combinatorial expressions for the stationary distribution. For permutations, this is a seemingly new multivariate generalization of the inversion polynomial.

17 pages, 1 figure, minor stylistic improvements

References in corpus (3)

• Multivariate Juggling Probabilities
• Geometric juggling with q-analogues
• Bumping sequences and multispecies juggling