NonHermitian tridiagonal random matrices and returns to the origin of a random walk
Abstract
We study a class of tridiagonal matrix models, the "qroots of unity" models, which includes the sign ($q=2$) and the clock ($q=\infty$) models by Feinberg and Zee. We find that the eigenvalue densities are bounded by and have the symmetries of the regular polygon with $2 q$ sides, in the complex plane. Furthermore the averaged traces of $M^k$ are integers that count closed random walks on the line, such that each site is visited a number of times multiple of $q$. We obtain an explicit evaluation for them.
 Publication:

arXiv eprints
 Pub Date:
 July 1999
 arXiv:
 arXiv:condmat/9907014
 Bibcode:
 1999cond.mat..7014C
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 14 pages including 5 figures