Further scaling exponents of random walks in random sceneries

A functional approach for random walks in random sceneries

A functional approach for the study of the random walks in random sceneries (RWRS) is proposed. Under fairly general assumptions on the random walk and on the random scenery, functional limit theorems are proved. The method allows to study separately the convergence of the walk and of the scenery: on the one hand, a general criterion for the convergence of the local time of the walk is provided...

Critical percolation in high dimensions: critical exponents, finite size scaling and random walks

First-Passage Exponents of Multiple Random Walks

We investigate first-passage statistics of an ensemble of N noninteracting random walks on a line. Starting from a configuration in which all particles are located in the positive half-line, we study Sn(t), the probability that the nth rightmost particle remains in the positive half-line up to time t. This quantity decays algebraically, Sn(t) ∼ tn , in the long-time limit. Interestingly, there ...

Scaling of star polymers: high order results

We extend existing renormalization group calculations for the exponents describing scaling of star polymers and polymer networks constituted by chains of different species (the so-called copolymer star exponents). Our four loop results find application in the description of various phenomena involving self-avoiding and random walks that interact.

Walking on fractals: diffusion and self-avoiding walks on percolation clusters

We consider random walks (RWs) and self-avoiding walks (SAWs) on disordered lattices directly at the percolation threshold. Applying numerical simulations, we study the scaling behavior of the models on the incipient percolation cluster in space dimensions d = 2, 3, 4. Our analysis yields estimates of universal exponents, governing the scaling laws for configurational properties of RWs and SAWs...