Tensor product Markov chains

Georgia Benkart, Persi Diaconis, Martin W. Liebeck, Pham Huu Tiep

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We analyze families of Markov chains that arise from decomposing tensor products of irreducible representations. This illuminates the Burnside-Brauer theorem for building irreducible representations, the McKay correspondence, and Pitman's 2M−X theorem. The chains are explicitly diagonalizable, and we use the eigenvalues/eigenvectors to give sharp rates of convergence for the associated random walks. For modular representations, the chains are not reversible, and the analytical details are surprisingly intricate. In the quantum group case, the chains fail to be diagonalizable, but a novel analysis using generalized eigenvectors proves successful.

Original languageEnglish (US)
Pages (from-to)17-83
Number of pages67
JournalJournal of Algebra
StatePublished - Nov 1 2020


  • Brauer character
  • Markov chain
  • McKay correspondence
  • Modular representation
  • Quantum group
  • Tensor product

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'Tensor product Markov chains'. Together they form a unique fingerprint.

Cite this