Random Walks on Figure Eight:From Polymers Through Chaos to Gravity and Beyond
This paper is extended and broadly generalized version of earlier published rapid communication, Phys.Rev.E, Vol.58, R 5213 (1998). It also elaborates on some problems which were left unsolved or just mentioned in Physics Reports Vol.298, 251 (1998). Applications of the obtained results include (but not limited to) polymer physics, classical and quantum chaos, fractional Hall effect, dynamics of textures in liquid crystals and 2+1 gravity. The paper presents some self contained excerpts from mathematics(not discussed so far in physics literature)to facilitate the uninterrupted reading of the manuscript.