Directed polymers and the quantum Toda lattice
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Mon, 22/11/2010 14:15 |
Neil O’Connell |
Stochastic Analysis Seminar  |
Eagle House |
| We relate the partition function associated with a certain Brownian directed polymer model to a diffusion process which is closely related to a quantum integrable system known as the quantum Toda lattice. This result is based on a `tropical' variant of a combinatorial bijection known as the Robinson-Schensted-Knuth (RSK) correspondence and is completely analogous to the relationship between the length of the longest increasing subsequence in a random permutation and the Plancherel measure on the dual of the symmetric group. | |||