Let { be a random walk in the domain of attraction of a stable law , i.e. there exists a sequence of positive real numbers ( ) such that / converges in law to . Our main result is that the rescaled process ( / , ≥0), when conditioned to stay positive, converges in law (in the functional sense) towards the corresponding stable Lévy process conditioned to stay positive. Under some additional assumptions,...
We consider a general discrete model for heterogeneous semiflexible polymer chains. Both the thermal noise and the inhomogeneous character of the chain (the ) are modeled in terms of random rotations. We focus on the regime, i.e., the analysis is performed for a given realization of the disorder. Semiflexible models differ substantially from random walks on short scales, but on large scales a brownian behavior emerges. By exploiting techniques from tensor analysis and non-commutative Fourier analysis,...
We consider a discrete-time version of the parabolic Anderson model. This may be described as a model for a directed -dimensional polymer interacting with a random potential, which is constant in the deterministic direction and i.i.d. in the orthogonal directions. The potential at each site is a positive random variable with a polynomial tail at infinity. We show that, as the size of the system diverges, the polymer extremity is localized almost surely at one single point which grows ballistically....
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