Random walks and orthogonal functions associated with highly symmetric graphs

The relationship of orthogonal functions associated with vertex transitive graphs and random walks on such graphs is investigated. We use this relations to characterize the exponentially decaying autocorrelation functions along random walks on isotropic random fields defined on vertex transitive graphs. The results are applied to a simple spin glass model.

[1]  N. Biggs.  THE TRAVELING SALESMAN PROBLEM A Guided Tour of Combinatorial Optimization , 1986 .

[2]  P. Diaconis,et al.  Generating a random permutation with random transpositions , 1981 .

[3]  A. Neumaier,et al.  Distance Regular Graphs , 1989 .

[4]  Correlation structure of the landscape of the graph-bipartitioning problem , 1992 .

[5]  S. Kirkpatrick,et al.  Solvable Model of a Spin-Glass , 1975 .

[6]  E D Weinberger,et al.  Why some fitness landscapes are fractal. , 1993, Journal of theoretical biology.

[7]  M. Mézard,et al.  Spin Glass Theory and Beyond , 1987 .

[8]  Jacobus H. van Lint,et al.  Introduction to Coding Theory , 1982 .

[9]  Eugene L. Lawler,et al.  A Guided Tour of Combinatorial Optimization , 1985 .

[10]  J. Besag.  Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[11]  P. Anderson,et al.  Application of statistical mechanics to NP-complete problems in combinatorial optimisation , 1986 .

[12]  Weinberger,et al.  RNA folding and combinatory landscapes. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  T. Koornwinder,et al.  Krawtchouk polynomials, a unification of two different group theoretic interpretations : (preprint) , 1982 .

[14]  P. Stadler,et al.  The landscape of the traveling salesman problem , 1992 .

[15]  P. Schuster,et al.  Statistics of landscapes based on free energies, replication and degradation rate constants of RNA secondary structures , 1991 .