Enumeration of simple random walks and tridiagonal matrices

Details Enumeration of simple random walks and tridiagonal matrices Enumeration of simple random walks and tridiagonal matrices

2000-11-21

arxiv.org/abs/cond-mat/0011360v2

J.Phys. A35 (2002) 1125-1146

Physics

Condensed Matter

Statistical Mechanics

several ref.and comments added, misprints corrected

Scientific paper

10.1088/0305-4470/35/5/302

We present some old and new results in the enumeration of random walks in one dimension, mostly developed in works of enumerative combinatorics. The relation between the trace of the $n$-th power of a tridiagonal matrix and the enumeration of weighted paths of $n$ steps allows an easier combinatorial enumeration of the paths. It also seems promising for the theory of tridiagonal random matrices .

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