Schur--Weyl duality for diagonalizing a Markov chain on the hypercube
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909977580404736 |
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| author | Diaconis, Persi Lin, Andrew Ram, Arun |
| author_facet | Diaconis, Persi Lin, Andrew Ram, Arun |
| contents | We show how the tools of modern algebraic combinatorics -- representation theory, Murphy elements, and particularly Schur--Weyl duality -- can be used to give an explicit orthonormal basis of eigenfunctions for a "curiously slowly mixing Markov chain" on the space of binary $n$-tuples. The basis is used to give sharp rates of convergence to stationarity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23285 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Schur--Weyl duality for diagonalizing a Markov chain on the hypercube Diaconis, Persi Lin, Andrew Ram, Arun Representation Theory Combinatorics Probability 20C30 (Primary) 60J10, 05E18 (Secondary) We show how the tools of modern algebraic combinatorics -- representation theory, Murphy elements, and particularly Schur--Weyl duality -- can be used to give an explicit orthonormal basis of eigenfunctions for a "curiously slowly mixing Markov chain" on the space of binary $n$-tuples. The basis is used to give sharp rates of convergence to stationarity. |
| title | Schur--Weyl duality for diagonalizing a Markov chain on the hypercube |
| topic | Representation Theory Combinatorics Probability 20C30 (Primary) 60J10, 05E18 (Secondary) |
| url | https://arxiv.org/abs/2512.23285 |