Probabilistic measures and algorithms arising from the Macdonald symmetric functions

Abstract

The Macdonald symmetric functions are used to define measures on the set of all partitions of all integers. Probabilistic algorithms are given for growing partitions according to these measures. The case of Hall-Littlewood polynomials is related to the finite classical groups, and the corresponding algorithms simplify. The case of Schur functions leads to a $q$-analog of Plancharel measure, and a conditioned version of the corresponding algorithms yields generalizations of the hook walk of combinatorics.

30 pages

References in corpus (1)

• A probabilistic approach toward the finite general linear and unitary groups

Cited by in corpus (6)

• Lectures on Integrable probability: Stochastic vertex models and symmetric functions
• Macdonald processes, quantum integrable systems and the Kardar-Parisi-Zhang universality class
• Law of Large Numbers for Infinite Random Matrices over a Finite Field
• A probabilistic approach toward the finite general linear and unitary groups
• Laguerre and Meixner orthogonal bases in the algebra of symmetric functions
• Cycle indices for the finite classical groups