Abstract
The statistics of meanders is studied in connection with the Temperley-Lieb algebra. Each (multi-component) meander corresponds to a pair of reduced elements of the algebra. The assignment of a weight q per connected component of meander translates into a bilinear form on the algebra, with a Gram matrix encoding the fine structure of meander numbers. Here, we calculate the associated Gram determinant as a function of q, and make use of the orthogonalization process to derive alternative expressions for meander numbers as sums over correlated random walks.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1-59 |
| Number of pages | 59 |
| Journal | Communications in Mathematical Physics |
| Volume | 186 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1997 |
| Externally published | Yes |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics