Analysis of random walks on a hexagonal lattice

Self-avoiding random walks on lattice strips.

A self-avoiding walk on an infinitely long lattice strip of finite width will asymptotically exhibit an end-to-end separation proportional to the number of steps. A proof of this proposition is presented together with comments concerning an earlier attempt to deal with the matter. In addition, some unproved, yet "obvious," conjectures concerning self-avoiding walks are cited as basic propositio...

Lattice paths and random walks

Lattice paths are ubiquitous in combinatorics and algorithmics, where they are either studied per se, or as a convenient encoding of other structures. Logically, they play an important role in Philippe’s papers. For instance, they are central in his combinatorial theory of continued fractions, to which Chapter 3 of this volume is devoted. In this chapter, we present a collection of seven papers...

Random Walks on Nite Convex Sets of Lattice Points

Dynamical Localization of Random Quantum Walks on the Lattice

The denomination Quantum Walks (QW for short) covers several variants of the definition we provide below . Informally, a QW describes the discrete time quantum dynamics of a particle with internal degree of freedom, the quantum walker, on a lattice. This dynamics consists in making the walker jump between neighboring sites of the lattice. The Hilbert space of the particle is the tensor product ...

Visible Lattice Points in Random Walks

We consider the possible visits to visible points of a random walker moving up and right in the integer lattice (with probability α and 1 − α, respectively) and starting from the origin. We show that, almost surely, the asymptotic proportion of strings of k consecutive visible lattice points visited by such an α-random walk is a certain constant ck(α), which is actually an (explicitly calculabl...