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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics